Algebra and Trigonometry (10th Edition)

Chapter 8

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; ; The circumference of a circle of radius is ... more

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. ; For uniform motion, the distance d covered in ... more

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Standard position ; If the vertex of an angle is ... more

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Central angle ; If the vertices of the initial and... more

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Since 1 degree is equal to revolution of a circle... more

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; The length of arc on a circle of radius and ... more

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Since radians is equal to revolution of a circle... more

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; A linear speed of an object is the distance ... more

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For a motion along the circle, an angular speed of... more

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For a motion along the circle, the linear speed ... more

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; An angle of is of a right angle.Draw the ... more

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; An angle of is of a right angle.Draw the ... more

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; An angle of consists of a rotation through ... more

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; An angle of consists of a clockwise rotation ... more

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; An angle of consists of 1 revolution followed ... more

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; An angle of consists of 1 revolution followed ... more

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; Convert the angle in radian to degree. ; An ... more

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; Convert the angle in radian to degree. ; An ... more

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; Convert the angle in radian to degree. ; An ... more

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; Convert the angle in radian to degree. ; An ... more

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; Convert the angle in radian to degree. ; The ... more

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; Convert the angle in radian to degree. ; The ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ;   ; Substitute for... more

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; Rewrite the given angle.  ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle. ; Substitute for ... more

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; Rewrite the given angle.  ; Substitute for ... more

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; Rewrite the given angle.  ; Substitute for ... more

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; Rewrite the given angle.  ; Substitute for ... more

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  ; Rewrite the given angle.  ; Substitute for ... more

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; Rewrite the given angle.  ; Substitute for ... more

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  ; Rewrite the given angle.  ; Substitute for ... more

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; Rewrite the given angle.  ; Substitute for ... more

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; Rewrite the given angle.  ; Substitute for ... more

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; Rewrite the given angle as the sum of degrees, ... more

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; Rewrite the given angle as the sum of degrees, ... more

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; Rewrite the given angle as the sum of degrees, ... more

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; Rewrite the given angle as the sum of degrees, ... more

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; Rewrite the given angle as the sum of degrees, ... more

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; Rewrite the given angle as the sum of degrees, ... more

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; Rewrite the expression as the sum of integers ... more

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; Rewrite the given angle as the sum of integers ... more

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; Rewrite the expression as the sum of integers ... more

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; Rewrite the expression as the sum of integers ... more

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; Rewrite the expression as the sum of integers ... more

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; Rewrite the expression as the sum of integers ... more

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5 meters ; Substitute 10 fo and for into the ... more

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12 feet ; Substitute 6 for and 2 for into the ... more

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6 feet ; Substitute 2 for and for into the arc ... more

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24 centimeters ; Substitute 6 for and for in ... more

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; Substitute 5 for and 3 for into the arc ... more

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; Substitute 6 for and 8 for into the arc ... more

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; Convert the angle given in degrees into ... more

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; Convert the angle given in degrees into ... more

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; Substitute 10 for and for into the sector ... more

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; Substitute 6 for and 2 for into the sector ... more

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; Substitute 2 for and for into the sector ... more

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; Substitute 6 for and for into the sector ... more

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; Substitute 5 for and 3 for into the sector ... more

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; Substitute 6 for and 8 for into the sector ... more

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; Convert the angle given in degrees into ... more

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; Convert the angle given in degrees to radians.... more

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: ; : ; Substitute 2 for and for   into the arc ... more

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: ; :   ; Substitute 4 for and for into the arc... more

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: ; :   ; Convert the angle given in degrees into... more

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: ; : ; Convert the angle given degrees into ... more

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; The central angle for 60 minutes (1 revolution... more

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; Convert the angle given in degrees into ... more

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  ; Convert the angle given in degrees into ... more

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; Convert the angle given in degrees into ... more

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  ; Convert the angle given in degrees into ... more

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  ; Substitute the sprinkler radius, 15, for and ... more

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; Convert the angle given in degree into radian.... more

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; Convert the angle given in degree into radian.... more

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Angular speed: ; Linear speed:   ; To calculate ... more

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Angular speed: ; Linear speed:   ; Substitute 5 ... more

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; To convert the angular speed of the drive in ... more

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; To convert the angular speed in revolution per ... more

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  ; To convert the angular speed of the drive in ... more

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; To convert the angular speed of the drive in ... more

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; Convert the linear speed in inches per minute ... more

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; ; Convert the angular speed of the car from ... more

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; Calculate the central angle between city M city... more

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; To calculate the central angle between city C ... more

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; The earth completes 1 revolution on its axis in... more

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; The earth completes 1 revolution on its axis in... more

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; To calculate the distance travelled by the moon... more

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; To calculate the distance travelled by earth in... more

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  ; Let the angular speed of 2-inch pulley be .... more

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Linear speed: ; Angular speed:   ; To calculate ... more

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  ; Convert the angular speed of the wheel from ... more

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; Convert the angular speed of the wheel from ... more

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; Convert the linear speed of the cable from ... more

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; To calculate the linear speed of the rays of ... more

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  ; The total area wandered by the dog is equal to... more

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  ; The central angle for the rectangle is ... more

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; The radius of the earth is 3960 miles.The earth... more

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; Convert the central angle from minute to radian... more

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Radius: ; Circumference: ; The circumference of ... more

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Entire Proof Answer:Use the linear speed formula ... more

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An angle measures in radian is easiest to define ... more

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1 radian is an angle subtended by an arc of a ... more

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1 radian is larger than 1 degree. ; In a complete ... more

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An angular speed of an object is the angle swept ... more

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True; the angle which is measure in degree can be ... more

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Nautical mile is used for navigating and charting.... more

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A 5-speed derailleur has 5 sprockets whereas a 9-... more

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The account for the difference is circular path.... more

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; Substitutes 0 for to calculate the zero of the ... more

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; Add to both sides of the given equation. ; ... more

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; To find the new function by shifting the graph ... more

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Horizontal asymptote: ; Vertical asymptote: ; In ... more

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; Substitute 6 for and 10 for into the ... more

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8 ; Substitute 5 for  into the given function. ; ... more

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complementary ; Two acute angles having sum , a ... more

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Cosine ; Consider that, in a right-angled triangle... more

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; The cofunctions of the complementary angles are... more

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Consider a right-angled triangle with the lengths ... more

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The trigonometric functions in a right triangle is... more

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The fundamental trigonometric identity is . So,  ... more

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Use the reciprocal identity of trigonometric ... more

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The tangent and cotangent function are cofunction ... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; ; : ; Use the Pythagorean theorem, , where... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; ;   ; Use the Pythagorean theorem, , where... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; ; ; Use the Pythagorean theorem, , where  ... more

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; ; ; ; Substitute the values of  and  into the ... more

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; ; ; ; Substitute the values of  and into the ... more

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; ; ; ; Substitute the values of  and into the ... more

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; ; ; ; Substitute the values of  and into the ... more

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; ; ; ; ; The trigonometric ratio , so according ... more

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; ; ;; ; Cosine function is the ratio of the ... more

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;; ; ; ; Cosine function is the ratio of the ... more

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;; ; ; ; Sine function is the ratio of the ... more

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:; : ; : ; : ; : ; Tangent function is the ratio ... more

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; ; ; ; ; Cotangent function is the ratio of the ... more

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;;;; ; Substitute 3 for  into the Pythagorean ... more

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;;;; ; Substitute 5 for  into the Pythagorean ... more

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;;;; ; Substitute  for  into the Pythagorean ... more

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;;;; ; Substitute  for  into the Pythagorean ... more

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;;;; ; Cosecant function is the ratio of the ... more

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;; ;; ; Cotangent function is the ratio of the ... more

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; Use the Pythagorean Identity, , to find the ... more

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1 ; Use the Pythagorean Identity, to find the ... more

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; Use the reciprocal identity, , to find the ... more

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; Use the reciprocal identity, , to find the ... more

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0 ; Use the quotient identity, , to find the value... more

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0 ; Use the quotient identity, , to find the value... more

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0 ; Use the theorem, , to find the value of the ... more

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0 ; Use the theorem, , to find the value of the ... more

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1 ; Use the theorem, , to find the value of the ... more

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1 ; Use the theorem, , to find the value of the ... more

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0 ; Use the Pythagorean Identity, , to rewrite the... more

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0 ; Use the Pythagorean Identity, , to rewrite the... more

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0 ; Use the theorem, , to simplify the given ... more

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0 ; Use the theorem, , to simplify the given ... more

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1 ; Use the complementary angle theorem, , to ... more

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1 ; Use the complementary angle theorem, .  ; Use ... more

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1 ; Use the complementary angle theorems, and... more

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1 ; Use the complementary angle theorems, and... more

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; Apply the complementary theorem, , into the ... more

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; Apply the complementary theorem, .Apply the ... more

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; Apply the complementary theorem, , into the ... more

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; Apply the trigonometric identity,, into the ... more

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; Substitute  for  into the given expression and ... more

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; Substitute  for  into the given expression and ... more

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; Substitute  for  into the given expression and ... more

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; Substitute  for  into the given expression and ... more

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; Substitute  for  into the given expression and ... more

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; Substitute  for  into the given expression and ... more

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In ,In ,In ,This implies that  ; Draw  ... more

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In In . ; Draw the perpendicular  on  axis.Draw ... more

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In , In ,  ; Let the radius of small circle be  ... more

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Entire Proof Answer: Convert this equation into ... more

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; ; ; ; ; Draw a triangle using the given ... more

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The value of lies between and 1, but is an ... more

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The value of ranges between and 1, for the ... more

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The sine function is the ratio of the length of ... more

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First method; It is easier to find out the values ... more

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; The argument of the given logarithmic function ... more

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,   ; A complex zero always occurs in pairs. This ... more

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; Apply remainder theorem, substitute  for  into ... more

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; Sketch a diagram with the help of the given ... more

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; Change MODE of graphing utility to radian and ... more

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Consider a right-angled triangle with an acute ... more

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For 3 acute angles, ,  and , the values of the ... more

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Since , use reciprocal identity,The option does ... more

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Set MODE of graphing utility to degrees and enter... more

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2 ; Since and , substitute 1 for  and for  into ... more

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2 ; Since and , substitute 1 for both and into ... more

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3 ; Since and , substitute 2 for and 1 for  into ... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to degrees.... more

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; Change MODE of the graphing utility to radians.... more

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; Change MODE of the graphing utility to radians.... more

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Leg1: ; Leg2: ; Let the opposite side of the given... more

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Range: ; Height:   ; Substitute the value for , ... more

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; Use the complementary angle property, . ; Use ... more

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; Draw the triangle with the provided values. ; ... more

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; Draw the triangle with the provided values. ; ... more

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; Draw the triangle with the provided values. ; ... more

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; Draw the triangle with the provided values. ; ... more

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; Draw the triangle with the provided values. ; ... more

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; Draw the triangle with the provided values. ; ... more

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; Draw the triangle with the provided values. ; ... more

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580 feet ; Let the height of balloon be .Draw a ... more

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; Draw a right-angled triangle with . ; Take  and... more

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; Draw a right triangle with the provided values... more

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; Use the labelled diagram of highway to find the... more

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from the upper left ;  Consider the ball hits on ... more

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·          As the angle approaches to , the value... more

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 Draw an equilateral triangle. Use the Pythagorean... more

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Assume the peak of the canyon is at 'N', and the ... more

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Assume the height of the building from the ground ... more

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All real numbers ; Apply the distributive property... more

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Vertex: ; axis of symmetry: ;  The vertex of the ... more

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tangent ; Consider the quadrants of the following ... more

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coterminal ; Two angles are coterminal, if they ... more

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; The measure of the terminal side of an angle ... more

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Since the angle lies in III quadrant, this ... more

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The value of  is 1 while the value of  is 0.Apply ... more

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The angle which measures the closest distance of a... more

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  ; The measure of the terminal side of an angle ... more

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In quadrant I, all the trigonometric functions are... more

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, ; The trigonometric function  is given as, . ... more

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The acute angle formed by the terminal sides of an... more

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; ; ;;; ; Draw the point on the rectangular ... more

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; ; ; ; ;  ; Draw the point on the rectangular ... more

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; ; ; ; ;  ; Draw the point on the rectangular ... more

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; ; ; ; ;  ; Draw the point on the rectangular ... more

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; ; ; ; ;  ; Draw the point on the rectangular ... more

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; ; ; ; ; ; Draw the point on the rectangular ... more

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; ; ; ; ;  ; Draw the point on the rectangular ... more

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; ; ; ; ; ; Plot the point on the rectangular ... more

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; ; ; ; ; ; Plot the point on the rectangular ... more

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; ; ; ; ;  ; Plot the point on the rectangular ... more

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  ; The angle  is positive and greater than .Draw ... more

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; The angle  is positive and greater than .Draw ... more

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; The angle  is positive and greater than .Draw ... more

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; The angle  is positive and greater than .Draw ... more

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  ; The angle  is positive and greater than .Draw ... more

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  ; The angle  is positive and greater than .Draw ... more

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; The angle  is positive and greater than .Draw ... more

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; The angle  is positive and greater than .Draw ... more

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; Draw the angle  . ; From the figure, the co-... more

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; Draw the angle . ; From the figure, the co-... more

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; The radian  is positive.Find the co-terminal ... more

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; Plot the angle  . ; From the figure, co-... more

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; Draw the graph representing signs of all ... more

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; Draw the graph representing signs of all ... more

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;  Draw the graph representing signs of all ... more

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; Draw the graph representing signs of all ... more

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; Draw the graph representing signs of all ... more

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;  Draw the graph representing signs of all ... more

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; Draw the graph representing signs of all ... more

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; Draw the graph representing signs of all ... more

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; The given angle lies in quadrant . Plot the ... more

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; The given angle  lies in quadrant .Plot the ... more

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; The given angle lies in quadrant .Plot the ... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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; Since  lies in quadrant , plot the angle of  in... more

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  ; Since  lies in quadrant , plot the angle of  ... more

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; Since  lies in quadrant , plot the angle of  in... more

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  ; Since  lies in quadrant , plot the angle of  ... more

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  ; Since  lies in quadrant , plot the angle of  ... more

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; Since  lies in quadrant , plot the angle of  in... more

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  ; Since  lies in quadrant , plot the angle of  ... more

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; Since  lies in quadrant and  is positive in ... more

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  ; Since the angle  lies in quadrant and  is ... more

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; The angle  lies in quadrant . Draw the angle of... more

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; The angle  lies in quadrant . Draw the angle of... more

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; The angle  lies in quadrant . Draw the angle of... more

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; The angle  lies in quadrant II. Draw the angle ... more

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; The angle  lies in quadrant . Draw the angle of... more

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  ; The angle  lies in quadrant . Draw the angle ... more

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; The angle  lies in quadrant . Draw the angle of... more

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1 ; The angle  lies in quadrant . Draw the angle ... more

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; The angle  lies in quadrant. Draw the angle of... more

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; The angle  lies in quadrant . Draw the angle of... more

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; The reference angle for is and . ; The angle... more

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; The reference angle for is and . ; The angle... more

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; The reference angle for is and . ; The angle... more

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; The reference angle for is and . ; The angle... more

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; The reference angle for is and . ; The angle... more

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; The reference angle for is and . ; The angle... more

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0 ; The reference angle for is 0 and . ; So, ; more

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1 ; The reference angle for is 0 and . ; The ... more

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0 ; The reference angle for  is 0 and . ; The ... more

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Undefined ; The reference angle for is 0 and ... more

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; Draw the given angle on the coordinate axis. ; ... more

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; Draw the given angle on the coordinate axis. ; ... more

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; ; ; ; ;  Since lies in Quadrant II, draw a ... more

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; ; ; ;  ; Since  lies in the quadrant IV, draw a ... more

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; ; ; ; ; Since lies in the quadrant III, draw a ... more

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; ; ; ; ; Since lies in the quadrant III, draw a ... more

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; ; ; ; Since lies in the quadrant II, draw a ... more

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; ; ; ; ; Since lies in the quadrant IV, draw a ... more

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; ; ; ; ; Since lies in the quadrant III, draw a ... more

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; ; ; ; ; Since lies in the quadrant III, draw a ... more

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; ; ; ; ; Since and in the quadrant II, draw a ... more

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; ; ; ; ; Since and in the quadrant III, draw a ... more

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; ; ; ; ; Since and is in the quadrant IV, draw ... more

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; ; ; ; ; Since and is in the quadrant II, draw ... more

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; ; ; ; ; Since and is in the quadrant III, draw... more

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; ; ; ; ; ; ; ; ; ; Find the values of the ... more

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; ; ; ; ;     Since and that means is in ... more

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; ; ; ; ; Since and that means is in quadrant ... more

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; ; ; ; ;    Since and that means is in ... more

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; ; ; ; ; Since and that means is in quadrant IV... more

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0 ; For angle , reference angle is  and  lies in ... more

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0 ; For angle , reference angle is  and  lies in ... more

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  ; In the given function the value of  is ... more

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; In the given function the value of  is positive... more

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3 ; In the given function, the value of  is ... more

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  ; is negative, and thus,  lies either in ... more

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; Determine  using the reciprocal identity... more

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; Determine using the reciprocal identity. ; The... more

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0 ; After the term, , write each sine function in ... more

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; Rewrite the given expression. ; Use the formula... more

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 Reference angle of , , and is , which is ... more

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There are various methods of calculating the exact... more

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For any given angle , reference angle is the acute... more

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