Question 1

Use the figure to find the exact value of the trigonometric function. ​
Sin 2θ​   ​
A = 1,b = 2
​

Accepted Answer

A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 4 } { 5 }$ ​ 
C)  $\frac { 5 } { 4 }$ ​ 
D)  $\frac { 5 } { 5 }$ ​ 
E)  $\frac { 5 } { 5 }$ ​ 
A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 4 } { 5 }$ ​ 
C)  $\frac { 5 } { 4 }$ ​ 
D)  $\frac { 5 } { 5 }$ ​ 
E)  $\frac { 5 } { 5 }$ ​ B

Question 2

The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v0 feet per second is $r = \frac { 1 } { 32 } v _ { 0 } ^ { 2 } \sin 2 \theta$ where r is measured in feet.A golfer strikes a golf ball at 90 feet per second.Ignoring the effects of air resistance,at what angle must the golfer hit the ball so that it travels 150 feet? (Round your answer to the nearest degree. )

Accepted Answer

A) 14° 
B) 36° 
C) 18° 
D) 27° 
E) 41° 
A) 14° 
B) 36° 
C) 18° 
D) 27° 
E) 41° C

Question 3

Use a double-angle formula to rewrite the expression. ​
10 cos2 x - 5
​

Accepted Answer

A) 5 cos x 
B) ​cos 5x 
C) ​10 cos 2x 
D) ​10 cos x 
E) ​5 cos 2x 
A) 5 cos x 
B) ​cos 5x 
C) ​10 cos 2x 
D) ​10 cos x 
E) ​5 cos 2x E

Question 4

Convert the expression.​ $$\sec \frac { b } { 2 }$$ ​

Accepted Answer

A) ​ $\pm \sqrt { \frac { 2 \tan b } { \tan b + \sin b } }$ 
B) ​ $\pm \sqrt { \frac { 2 \tan b } { \tan b + \csc b } }$ 
C) ​ $\pm \sqrt { \frac { \tan b } { \tan b - \sin b } }$ ​ 
D) ​ $\pm \sqrt { \frac { \tan b } { \tan b + \sin b } }$ 
E) ​ $\pm \sqrt { \frac { 2 \tan b } { \tan b - \sin b } }$ 
A) ​ $\pm \sqrt { \frac { 2 \tan b } { \tan b + \sin b } }$ 
B) ​ $\pm \sqrt { \frac { 2 \tan b } { \tan b + \csc b } }$ 
C) ​ $\pm \sqrt { \frac { \tan b } { \tan b - \sin b } }$ ​ 
D) ​ $\pm \sqrt { \frac { \tan b } { \tan b + \sin b } }$ 
E) ​ $\pm \sqrt { \frac { 2 \tan b } { \tan b - \sin b } }$

Question 5

Convert the expression. ​​ $$1 + \cos 4 y$$ ​

Accepted Answer

A)  $2 \cos ^ { 2 } 2 y$ 
B) ​ $\cos ^ { 2 } 4 y$ 
C) ​ $\cos ^ { 2 } 2 y$ 
D) ​ $4 \cos ^ { 2 } 4 y$ 
E) ​ $2 \cos ^ { 2 } 4 y$ 
A)  $2 \cos ^ { 2 } 2 y$ 
B) ​ $\cos ^ { 2 } 4 y$ 
C) ​ $\cos ^ { 2 } 2 y$ 
D) ​ $4 \cos ^ { 2 } 4 y$ 
E) ​ $2 \cos ^ { 2 } 4 y$

Question 6

The mach number M of an airplane is the ratio of its speed to the speed of sound.When an airplane travels faster than the speed of sound,the sound waves form a cone behind the airplane (see figure).The mach number is related to the apex angle θ of the cone by $$\sin ( \theta / 5 ) = 1 / M$$ .​   ​ Rewrite the equation in terms of θ.
​

Accepted Answer

A) ​ $\theta = 5 \sin \left( \frac { 1 } { M } \right)$ 
B) ​ $\theta = \sin \left( \frac { 1 } { M } \right)$ 
C) ​ $\theta = \sin ^ { - 1 } \left( \frac { 1 } { M } \right)$ 
D) ​ $\theta = 5 \sin ^ { - 1 } \left( \frac { 5 } { M } \right)$ 
E)  $\theta = 5 \sin ^ { - 1 } \left( \frac { 1 } { M } \right)$ 
A) ​ $\theta = 5 \sin \left( \frac { 1 } { M } \right)$ 
B) ​ $\theta = \sin \left( \frac { 1 } { M } \right)$ 
C) ​ $\theta = \sin ^ { - 1 } \left( \frac { 1 } { M } \right)$ 
D) ​ $\theta = 5 \sin ^ { - 1 } \left( \frac { 5 } { M } \right)$ 
E)  $\theta = 5 \sin ^ { - 1 } \left( \frac { 1 } { M } \right)$

Question 7

Use the figure to find the exact value of the trigonometric function. ​
Sec 2θ​   ​
A = 1,b = 8
​

Accepted Answer

A) ​ $\frac { 63 } { 64 }$ 
B)  $\frac { 63 } { 65 }$ 
C) ​ $\frac { 64 } { 65 }$ 
D) ​ $\frac { 65 } { 63 }$ 
E)  $\frac { 65 } { 64 }$ 
A) ​ $\frac { 63 } { 64 }$ 
B)  $\frac { 63 } { 65 }$ 
C) ​ $\frac { 64 } { 65 }$ 
D) ​ $\frac { 65 } { 63 }$ 
E)  $\frac { 65 } { 64 }$

Question 8

Find all solutions of the given equation in the interval [0,2π). ​​ $$\cos 3 x = \cos x$$ ​

Accepted Answer

A) ​ $x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$ 
B) ​ $x = \frac { \pi } { 4 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C) ​ $x = 0 , \frac { \pi } { 4 } , \frac { \pi } { 2 } , \pi$ 
D) ​ $x = 0 , \frac { \pi } { 4 } , \pi , \frac { 3 \pi } { 4 }$ 
E) ​ $x = \frac { \pi } { 8 } , \frac { 2 \pi } { 8 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 8 } , \pi , \frac { 3 \pi } { 2 }$ 
A) ​ $x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$ 
B) ​ $x = \frac { \pi } { 4 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C) ​ $x = 0 , \frac { \pi } { 4 } , \frac { \pi } { 2 } , \pi$ 
D) ​ $x = 0 , \frac { \pi } { 4 } , \pi , \frac { 3 \pi } { 4 }$ 
E) ​ $x = \frac { \pi } { 8 } , \frac { 2 \pi } { 8 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 8 } , \pi , \frac { 3 \pi } { 2 }$

Question 9

Use the half-angle formula to simplify the given expression. ​​ $$\sqrt { \frac { 1 + \cos 8 x } { 2 } }$$ ​

Accepted Answer

A) ​​cos |2x| 
B) ​​cos |8x| 
C) ​​cos |16x| 
D) ​​cos |32x| 
E) ​cos |4x| 
A) ​​cos |2x| 
B) ​​cos |8x| 
C) ​​cos |16x| 
D) ​​cos |32x| 
E) ​cos |4x|

Question 10

Use the half-angle formulas to simplify the expression.​ $$- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }$$ ​

Accepted Answer

A) ​ $- \left| \sin \left( \frac { x - 3 } { 2 } \right) \right|$ 
B) ​ $- \left| \sin ^ { - 1 } \left( \frac { x + 3 } { 2 } \right) \right|$ 
C) ​ $- | \sin ( x - 3 ) |$ 
D) ​ $- \left| \sin ^ { - 1 } \left( \frac { x - 3 } { 2 } \right) \right|$ 
E) ​ $- \left| \sin \left( \frac { x + 3 } { 2 } \right) \right|$ 
A) ​ $- \left| \sin \left( \frac { x - 3 } { 2 } \right) \right|$ 
B) ​ $- \left| \sin ^ { - 1 } \left( \frac { x + 3 } { 2 } \right) \right|$ 
C) ​ $- | \sin ( x - 3 ) |$ 
D) ​ $- \left| \sin ^ { - 1 } \left( \frac { x - 3 } { 2 } \right) \right|$ 
E) ​ $- \left| \sin \left( \frac { x + 3 } { 2 } \right) \right|$

Question 11

Use a double-angle formula to find the exact value of cos2u when​ $$\sin u = \frac { 7 } { 25 } \text {, where } \frac { \pi } { 2 } < u < \pi$$

Accepted Answer

A)  $\cos 2 u = \frac { 527 } { 625 }$ 
B) ​ $\cos 2 u = - \frac { 1152 } { 625 }$ 
C) ​ $\cos 2 u = \frac { 336 } { 625 }$ 
D) ​ $\cos 2 u = \frac { 168 } { 625 }$ 
E) ​ $\cos 2 u = - \frac { 478 } { 625 }$ 
A)  $\cos 2 u = \frac { 527 } { 625 }$ 
B) ​ $\cos 2 u = - \frac { 1152 } { 625 }$ 
C) ​ $\cos 2 u = \frac { 336 } { 625 }$ 
D) ​ $\cos 2 u = \frac { 168 } { 625 }$ 
E) ​ $\cos 2 u = - \frac { 478 } { 625 }$

Question 12

Use the figure to find the exact value of the trigonometric function.​   $\begin{array} { l } 
a = 8 , b = 9 \
c = 2 , d = 5
\end{array}$ ​ sin 2α
​

Accepted Answer

A) ​ $\frac { 8 } { 145 }$ 
B) ​ $\frac { 9 } { 145 }$ 
C) ​ $\frac { 145 } { 2 }$ ​ 
D) ​ $\frac { 145 } { 144 }$ 
E)  $\frac { 144 } { 145 }$ 
A) ​ $\frac { 8 } { 145 }$ 
B) ​ $\frac { 9 } { 145 }$ 
C) ​ $\frac { 145 } { 2 }$ ​ 
D) ​ $\frac { 145 } { 144 }$ 
E)  $\frac { 144 } { 145 }$

Question 13

Use the product-to-sum formulas to rewrite the product as a sum or difference.​ $$\sin \frac { \pi } { 3 } \cos \frac { \pi } { 6 }$$ ​

Accepted Answer

A) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } + \cos \frac { \pi } { 6 } \right)$ 
B) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } + \sin \frac { \pi } { 6 } \right)$ 
C) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } - \cos \frac { \pi } { 6 } \right)$ 
D) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } - \sin \frac { \pi } { 6 } \right)$ 
E) ​ $\left( \sin \frac { \pi } { 2 } + \cos \frac { \pi } { 6 } \right)$ 
A) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } + \cos \frac { \pi } { 6 } \right)$ 
B) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } + \sin \frac { \pi } { 6 } \right)$ 
C) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } - \cos \frac { \pi } { 6 } \right)$ 
D) ​ $\frac { 1 } { 2 } \left( \sin \frac { \pi } { 2 } - \sin \frac { \pi } { 6 } \right)$ 
E) ​ $\left( \sin \frac { \pi } { 2 } + \cos \frac { \pi } { 6 } \right)$

Question 14

Use the product-to-sum formulas to rewrite the product as a sum or difference.​ $$4 \cos \frac { \pi } { 2 } \sin \frac { 5 \pi } { 4 }$$ ​

Accepted Answer

A) ​ $2 \left( \sin \frac { 7 \pi } { 4 } - \sin \frac { 3 \pi } { 4 } \right)$ 
B) ​ $2 \left( \cos \frac { 7 \pi } { 4 } - \cos \frac { 3 \pi } { 4 } \right)$ 
C) ​ $2 \left( \sin \frac { 7 \pi } { 4 } + \cos \frac { 3 \pi } { 4 } \right)$ 
D) ​ $2 \left( \sin \frac { 7 \pi } { 4 } + \sin \frac { 3 \pi } { 4 } \right)$ 
E) ​ $2 \left( \cos \frac { 7 \pi } { 4 } + \cos \frac { 3 \pi } { 4 } \right)$ 
A) ​ $2 \left( \sin \frac { 7 \pi } { 4 } - \sin \frac { 3 \pi } { 4 } \right)$ 
B) ​ $2 \left( \cos \frac { 7 \pi } { 4 } - \cos \frac { 3 \pi } { 4 } \right)$ 
C) ​ $2 \left( \sin \frac { 7 \pi } { 4 } + \cos \frac { 3 \pi } { 4 } \right)$ 
D) ​ $2 \left( \sin \frac { 7 \pi } { 4 } + \sin \frac { 3 \pi } { 4 } \right)$ 
E) ​ $2 \left( \cos \frac { 7 \pi } { 4 } + \cos \frac { 3 \pi } { 4 } \right)$

Question 15

Use the figure below to determine the exact value of the given function.​ $$\csc 2 \theta$$

Accepted Answer

A) ​ $\csc 2 \theta = \frac { 13 } { 5 }$ 
B) ​ $\csc 2 \theta = \frac { 13 } { 7 }$ 
C) ​ $\csc 2 \theta = \frac { 13 } { 5 }$ 
D) ​ $\csc 2 \theta = \frac { 13 } { 9 }$ 
E) ​ $\csc 2 \theta = \frac { 13 } { 12 }$ 
A) ​ $\csc 2 \theta = \frac { 13 } { 5 }$ 
B) ​ $\csc 2 \theta = \frac { 13 } { 7 }$ 
C) ​ $\csc 2 \theta = \frac { 13 } { 5 }$ 
D) ​ $\csc 2 \theta = \frac { 13 } { 9 }$ 
E) ​ $\csc 2 \theta = \frac { 13 } { 12 }$

Question 16

Use the figure to find the exact value of the trigonometric function. ​
Cos 2θ​   ​
A = 1,b = 2
​

Accepted Answer

A) ​ $\frac { 3 } { 4 }$ 
B)  $\frac { 3 } { 5 }$ 
C) ​ $\frac { 5 } { 3 }$ 
D) ​ $\frac { 4 } { 5 }$ 
E) ​ $\frac { 5 } { 4 }$ 
A) ​ $\frac { 3 } { 4 }$ 
B)  $\frac { 3 } { 5 }$ 
C) ​ $\frac { 5 } { 3 }$ 
D) ​ $\frac { 4 } { 5 }$ 
E) ​ $\frac { 5 } { 4 }$

Question 17

Use the sum-to-product formulas to find the exact value of the given expression. ​​ $$\cos 150 ^ { \circ } + \cos 30 ^ { \circ }$$ ​

Accepted Answer

A) ​ $\frac { - \sqrt { 3 } } { 2 }$ 
B) ​1 
C) ​ $\frac { \sqrt { 3 } } { 2 }$ 
D) -1 
E) 0 
A) ​ $\frac { - \sqrt { 3 } } { 2 }$ 
B) ​1 
C) ​ $\frac { \sqrt { 3 } } { 2 }$ 
D) -1 
E) 0

Question 18

Use the sum-to-product formulas to rewrite the sum or difference as a product.​ $$\sin 9 \theta + \sin 7 \theta$$ ​

Accepted Answer

A) ​ $2 \sin 8 \theta \sin \theta$ 
B) ​ $2 \cos 8 \theta \cos \theta$ 
C) ​ $2 \sin 8 \theta \cos \theta$ ​ 
D) ​ $2 \cos 8 \theta \sin \theta$ 
E) ​ $2 \sin 9 \theta \cos 7 \theta$ 
A) ​ $2 \sin 8 \theta \sin \theta$ 
B) ​ $2 \cos 8 \theta \cos \theta$ 
C) ​ $2 \sin 8 \theta \cos \theta$ ​ 
D) ​ $2 \cos 8 \theta \sin \theta$ 
E) ​ $2 \sin 9 \theta \cos 7 \theta$

Question 19

Find the exact solutions of the given equation in the interval [0,2π).​ $$\cos 2 x + 3 \cos x + 2 = 0$$

Accepted Answer

A) ​ $x = 0 , \pi , \frac { 2 \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
B) ​ $x = \pi , \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
C) ​ $x = \pi , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 }$ 
D) ​x = 0 
E) ​ $x = 0 , \pi , \frac { \pi } { 3 } , \frac { 4 \pi } { 3 }$ 
A) ​ $x = 0 , \pi , \frac { 2 \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
B) ​ $x = \pi , \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
C) ​ $x = \pi , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 }$ 
D) ​x = 0 
E) ​ $x = 0 , \pi , \frac { \pi } { 3 } , \frac { 4 \pi } { 3 }$

Question 20

Use the product-to-sum formulas to rewrite the product as a sum or difference.​ $$8 \sin 65 ^ { \circ } \cos 25 ^ { \circ }$$ ​

Accepted Answer

A) ​ $8 \left( \sin 90 ^ { \circ } + \sin 40 ^ { \circ } \right)$ 
B) ​ $4 \left( \cos 90 ^ { \circ } + \cos 40 ^ { \circ } \right)$ 
C) ​ $4 \left( \cos 90 ^ { \circ } - \cos 40 ^ { \circ } \right)$ 
D) ​ $\left( \sin 90 ^ { \circ } + \sin 40 ^ { \circ } \right)$ 
E) ​ $4 \left( \sin 90 ^ { \circ } + \sin 40 ^ { \circ } \right)$ 
A) ​ $8 \left( \sin 90 ^ { \circ } + \sin 40 ^ { \circ } \right)$ 
B) ​ $4 \left( \cos 90 ^ { \circ } + \cos 40 ^ { \circ } \right)$ 
C) ​ $4 \left( \cos 90 ^ { \circ } - \cos 40 ^ { \circ } \right)$ 
D) ​ $\left( \sin 90 ^ { \circ } + \sin 40 ^ { \circ } \right)$ 
E) ​ $4 \left( \sin 90 ^ { \circ } + \sin 40 ^ { \circ } \right)$

Exam 35: Multiple Angle and Product to Sum Formulas

Use the figure to find the exact value of the trigonometric function. ​ Sin 2θ​ ​ A = 1,b = 2 ​

Use a double-angle formula to rewrite the expression. ​ 10 cos2 x - 5 ​

Convert the expression.​ sec⁡b2\sec \frac { b } { 2 }sec2b​ ​

Convert the expression. ​​ 1+cos⁡4y1 + \cos 4 y1+cos4y ​

Use the figure to find the exact value of the trigonometric function. ​ Sec 2θ​ ​ A = 1,b = 8 ​

Find all solutions of the given equation in the interval [0,2π). ​​ cos⁡3x=cos⁡x\cos 3 x = \cos xcos3x=cosx ​

Use the half-angle formula to simplify the given expression. ​​ 1+cos⁡8x2\sqrt { \frac { 1 + \cos 8 x } { 2 } }21+cos8x​​ ​

Use the half-angle formulas to simplify the expression.​ −1−cos⁡(x−3)2- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }−21−cos(x−3)​​ ​

Use a double-angle formula to find the exact value of cos2u when​ sin⁡u=725, where π2<u<π\sin u = \frac { 7 } { 25 } \text {, where } \frac { \pi } { 2 } < u < \pisinu=257​, where 2π​<u<π

Use the figure to find the exact value of the trigonometric function.​ a=8,b=9 c=2,d=5 ​ sin 2α ​

Use the product-to-sum formulas to rewrite the product as a sum or difference.​ sin⁡π3cos⁡π6\sin \frac { \pi } { 3 } \cos \frac { \pi } { 6 }sin3π​cos6π​ ​

Use the product-to-sum formulas to rewrite the product as a sum or difference.​ 4cos⁡π2sin⁡5π44 \cos \frac { \pi } { 2 } \sin \frac { 5 \pi } { 4 }4cos2π​sin45π​ ​

Use the figure below to determine the exact value of the given function.​ csc⁡2θ\csc 2 \thetacsc2θ

Use the figure to find the exact value of the trigonometric function. ​ Cos 2θ​ ​ A = 1,b = 2 ​

Use the sum-to-product formulas to find the exact value of the given expression. ​​ cos⁡150∘+cos⁡30∘\cos 150 ^ { \circ } + \cos 30 ^ { \circ }cos150∘+cos30∘ ​

Use the sum-to-product formulas to rewrite the sum or difference as a product.​ sin⁡9θ+sin⁡7θ\sin 9 \theta + \sin 7 \thetasin9θ+sin7θ ​

Find the exact solutions of the given equation in the interval [0,2π).​ cos⁡2x+3cos⁡x+2=0\cos 2 x + 3 \cos x + 2 = 0cos2x+3cosx+2=0

Use the product-to-sum formulas to rewrite the product as a sum or difference.​ 8sin⁡65∘cos⁡25∘8 \sin 65 ^ { \circ } \cos 25 ^ { \circ }8sin65∘cos25∘ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Use the figure to find the exact value of the trigonometric function. Sin 2θ A = 1,b = 2

Use a double-angle formula to rewrite the expression. 10 cos²x - 5

Convert the expression. $\sec \frac { b } { 2 }$

Convert the expression. $1 + \cos 4 y$

Use the figure to find the exact value of the trigonometric function. Sec 2θ A = 1,b = 8

Find all solutions of the given equation in the interval [0,2π). $\cos 3 x = \cos x$

Use the half-angle formula to simplify the given expression. $\sqrt { \frac { 1 + \cos 8 x } { 2 } }$

Use the half-angle formulas to simplify the expression. $- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }$

Use a double-angle formula to find the exact value of cos2u when $\sin u = \frac { 7 } { 25 } \text {, where } \frac { \pi } { 2 } < u < \pi$

Use the figure to find the exact value of the trigonometric function. $Use the figure to find the exact value of the trigonometric function. \begin{array} { l } a = 8 , b = 9 \\ c = 2 , d = 5 \end{array} sin 2α $ a=8,b=9 c=2,d=5 sin 2α

Use the product-to-sum formulas to rewrite the product as a sum or difference. $\sin \frac { \pi } { 3 } \cos \frac { \pi } { 6 }$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $4 \cos \frac { \pi } { 2 } \sin \frac { 5 \pi } { 4 }$

Use the figure below to determine the exact value of the given function. $\csc 2 \theta$ $Use the figure below to determine the exact value of the given function. \csc 2 \theta$

Use the figure to find the exact value of the trigonometric function. Cos 2θ A = 1,b = 2

Use the sum-to-product formulas to find the exact value of the given expression. $\cos 150 ^ { \circ } + \cos 30 ^ { \circ }$

Use the sum-to-product formulas to rewrite the sum or difference as a product. $\sin 9 \theta + \sin 7 \theta$

Find the exact solutions of the given equation in the interval [0,2π). $\cos 2 x + 3 \cos x + 2 = 0$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $8 \sin 65 ^ { \circ } \cos 25 ^ { \circ }$