Question 1

Solve the following equation. 
$4 \sin ^ { 2 } x = 12 \cos ^ { 2 } x$

Accepted Answer

A)  $\frac { 2 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
B)  $\frac { \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
C)  $\frac { \pi } { 3 } + n \pi , \frac { \pi } { 3 } + n \pi$ 
D)  $\frac { 4 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
E)  $\frac { \pi } { 2 } + n \pi , \frac { 2 \pi } { 5 } + n \pi$ 
A)  $\frac { 2 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
B)  $\frac { \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
C)  $\frac { \pi } { 3 } + n \pi , \frac { \pi } { 3 } + n \pi$ 
D)  $\frac { 4 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
E)  $\frac { \pi } { 2 } + n \pi , \frac { 2 \pi } { 5 } + n \pi$

Question 2

Given $a = 9 , b = 11 , \text { and } c = 6$ , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.

Accepted Answer

A)  $54.85 ^ { \circ }$ 
B)  $33.03 ^ { \circ }$ 
C)  $80.44 ^ { \circ }$ 
D)  $92.12 ^ { \circ }$ 
E)  $60.33 ^ { \circ }$ 
A)  $54.85 ^ { \circ }$ 
B)  $33.03 ^ { \circ }$ 
C)  $80.44 ^ { \circ }$ 
D)  $92.12 ^ { \circ }$ 
E)  $60.33 ^ { \circ }$

Question 3

Find the rate of change of the function $f ( x ) = - x + \sin x$

Accepted Answer

A)  $\tan x \sec x - x$ 
B)  $\cos x + 1$ 
C)  $\cos x - 1$ 
D)  $- \cos x - 1$ 
E)  $- \cos x + 1$ 
A)  $\tan x \sec x - x$ 
B)  $\cos x + 1$ 
C)  $\cos x - 1$ 
D)  $- \cos x - 1$ 
E)  $- \cos x + 1$

Question 4

Use the half-angle formulas to determine the exact value of the given trigonometric expression. $\tan \frac { 3 \pi } { 8 }$

Accepted Answer

A)  $\quad \tan \frac { 3 \pi } { 8 } = \sqrt { 2 } - 1$ 
B) $\tan \frac { 3 \pi } { 8 } = \frac { \sqrt { 2 + \sqrt { 2 } } } { 4 }$ 
C)  $\tan \frac { 3 \pi } { 8 } = \sqrt { 2 } + 1$ 
D) $\tan \frac { 3 \pi } { 8 } = - \frac { \sqrt { 2 - \sqrt { 2 } } } { 4 }$ 
E)  $\tan \frac { 3 \pi } { 8 } = \sqrt { 2 - \sqrt { 2 } }$ 
A)  $\quad \tan \frac { 3 \pi } { 8 } = \sqrt { 2 } - 1$ 
B) $\tan \frac { 3 \pi } { 8 } = \frac { \sqrt { 2 + \sqrt { 2 } } } { 4 }$ 
C)  $\tan \frac { 3 \pi } { 8 } = \sqrt { 2 } + 1$ 
D) $\tan \frac { 3 \pi } { 8 } = - \frac { \sqrt { 2 - \sqrt { 2 } } } { 4 }$ 
E)  $\tan \frac { 3 \pi } { 8 } = \sqrt { 2 - \sqrt { 2 } }$

Question 5

A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this Motion is modeled by where is the distance from equilibrium (in feet) and is the time (in seconds). 
$y = \frac { 1 } { 8 } \sin 2 t + \frac { 1 } { 6 } \cos 2 t$ 
Use the identity
$a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$
where $C = \arctan ( b / a ) , a > 0$, to write the model in the form $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B t + C )$.

Accepted Answer

A)  $y = \frac { 5 } { 24 } \sin ( 2 t + 0.9273 )$ 
B)  $y = \frac { 24 } { 5 } \sin ( 2 t - 0.9273 )$ 
C)  $y = \frac { 24 } { 5 } \sin ( 2 t + 0.9273 )$ 
D)  $y = \sin ( 2 t - 0.9273 )$ 
E)  $y = \sin ( 2 t + 0.9273 )$ 
A)  $y = \frac { 5 } { 24 } \sin ( 2 t + 0.9273 )$ 
B)  $y = \frac { 24 } { 5 } \sin ( 2 t - 0.9273 )$ 
C)  $y = \frac { 24 } { 5 } \sin ( 2 t + 0.9273 )$ 
D)  $y = \sin ( 2 t - 0.9273 )$ 
E)  $y = \sin ( 2 t + 0.9273 )$

Question 6

Use the given values to evaluate (if possible) three trigonometric functions cosec $\theta$ $\tan \theta , \cos \theta$ $\sin \theta = - 4 , \quad \cot \theta = 0$

Accepted Answer

A)  $\csc \theta = - \frac { 1 } { 4 }$ 
$\tan \theta$ is undefined.
 $\cos \theta = 0$ 
B)  $\csc \theta = \frac { 1 } { 4 }$ 
$\tan \theta$ is undefined. 
$\cos \theta = - \sqrt { 15 }$ 
C)  $\csc \theta = - \frac { 1 } { 4 }$ 
$\tan \theta$ is undefined. 
$\cos \theta = - \sqrt { 15 }$ 
D)  $\csc \theta = \frac { 1 } { 4 }$
 $\tan \theta$ is undefined. 
$\cos \theta = \sqrt { 15 }$ 
E)  $\csc \theta$ is undefined.
$\tan \theta = \frac { 1 } { 4 }$
$\cos \theta = - \sqrt { 15 }$ 
A)  $\csc \theta = - \frac { 1 } { 4 }$ 
$\tan \theta$ is undefined.
 $\cos \theta = 0$ 
B)  $\csc \theta = \frac { 1 } { 4 }$ 
$\tan \theta$ is undefined. 
$\cos \theta = - \sqrt { 15 }$ 
C)  $\csc \theta = - \frac { 1 } { 4 }$ 
$\tan \theta$ is undefined. 
$\cos \theta = - \sqrt { 15 }$ 
D)  $\csc \theta = \frac { 1 } { 4 }$
 $\tan \theta$ is undefined. 
$\cos \theta = \sqrt { 15 }$ 
E)  $\csc \theta$ is undefined.
$\tan \theta = \frac { 1 } { 4 }$
$\cos \theta = - \sqrt { 15 }$

Question 7

Use the sum-to-product formulas to select the sum or difference as a product. 
$\cos 3 \theta + \cos 6 \theta$

Accepted Answer

A)  $2 \cos \frac { 9 \theta } { 2 } \cos \left( - \frac { 3 \theta } { 2 } \right)$ 
B)  $2 \cos \frac { 9 \theta } { 2 } \sin \left( - \frac { 3 \theta } { 2 } \right)$ 
C)  $2 \cos \frac { 9 \theta } { 2 } \cos \left( \frac { 3 \theta } { 2 } \right)$ 
D)  $2 \cos \left( - \frac { 9 \theta } { 2 } \right) \cos \frac { 3 \theta } { 2 }$ 
E)  $2 \cos \frac { 9 \theta } { 2 } \sin \left( \frac { 3 \theta } { 2 } \right)$ 
A)  $2 \cos \frac { 9 \theta } { 2 } \cos \left( - \frac { 3 \theta } { 2 } \right)$ 
B)  $2 \cos \frac { 9 \theta } { 2 } \sin \left( - \frac { 3 \theta } { 2 } \right)$ 
C)  $2 \cos \frac { 9 \theta } { 2 } \cos \left( \frac { 3 \theta } { 2 } \right)$ 
D)  $2 \cos \left( - \frac { 9 \theta } { 2 } \right) \cos \frac { 3 \theta } { 2 }$ 
E)  $2 \cos \frac { 9 \theta } { 2 } \sin \left( \frac { 3 \theta } { 2 } \right)$

Question 8

Evaluate the following expression. $\frac { 3 + 3 \sin 3 \theta } { \cos 3 \theta } + \frac { 3 \cos 3 \theta } { 1 + \sin 3 \theta }$

Accepted Answer

A)  $6 \sec 3 \theta$ 
B)  $- 6 \sec 3 \theta$ 
C)  $\sec 6 \theta$ 
D)  $3 \sec 3 \theta$ 
E)  $- 3 \sec 3 \theta$ 
A)  $6 \sec 3 \theta$ 
B)  $- 6 \sec 3 \theta$ 
C)  $\sec 6 \theta$ 
D)  $3 \sec 3 \theta$ 
E)  $- 3 \sec 3 \theta$

Question 9

Evaluate the expression. $\cos 10 \alpha$

Accepted Answer

A)  $\cos ^ { 2 } 5 \alpha + \sin ^ { 2 } 5 \alpha$ 
B)  $\cos ^ { 4 } 5 \alpha + \sin ^ { 4 } 5 \alpha$ 
C)  $\cos ^ { 4 } 5 \alpha - \sin ^ { 4 } 5 \alpha$ 
D)  $\cos ^ { 2 } 5 \alpha - \sin ^ { 2 } 5 \alpha$ 
E)  $\cos ^ { 4 } 5 \alpha - \sin ^ { 2 } 5 \alpha$ 
A)  $\cos ^ { 2 } 5 \alpha + \sin ^ { 2 } 5 \alpha$ 
B)  $\cos ^ { 4 } 5 \alpha + \sin ^ { 4 } 5 \alpha$ 
C)  $\cos ^ { 4 } 5 \alpha - \sin ^ { 4 } 5 \alpha$ 
D)  $\cos ^ { 2 } 5 \alpha - \sin ^ { 2 } 5 \alpha$ 
E)  $\cos ^ { 4 } 5 \alpha - \sin ^ { 2 } 5 \alpha$

Question 10

Use a double-angle formula to rewrite the expression. 
$6 \sin ^ { 2 } x - 3$

Accepted Answer

A)  $- 3 \cos 2 x$ 
B)  $3 \cos 2 x$ 
C)  $- 6 \cos x$ 
D)  $3 \cos x$ 
E)  $6 \cos 2 x$ 
A)  $- 3 \cos 2 x$ 
B)  $3 \cos 2 x$ 
C)  $- 6 \cos x$ 
D)  $3 \cos x$ 
E)  $6 \cos 2 x$

Question 11

Use the Law of Sines to solve (if possible) the triangle. Round your answers to two decimal places. $A = 76 ^ { \circ } , a = 102 , b = 63$

Accepted Answer

A)  $ B \approx - 67 ^ { \circ } , C \approx 37 ^ { \circ } , c \approx 96.9$ 
B)  $B \approx 73.2 ^ { \circ } , C \approx 30.8 ^ { \circ } , c \approx 96.9$ 
C)  $B \approx 36.82 ^ { \circ } , C \approx 67.18 ^ { \circ } , c \approx 96.9$ 
D)  $B \approx 67.18 ^ { \circ } , C \approx 36.82 ^ { \circ } , c \approx 96.9$ 
E)  No Solution 
A)  $ B \approx - 67 ^ { \circ } , C \approx 37 ^ { \circ } , c \approx 96.9$ 
B)  $B \approx 73.2 ^ { \circ } , C \approx 30.8 ^ { \circ } , c \approx 96.9$ 
C)  $B \approx 36.82 ^ { \circ } , C \approx 67.18 ^ { \circ } , c \approx 96.9$ 
D)  $B \approx 67.18 ^ { \circ } , C \approx 36.82 ^ { \circ } , c \approx 96.9$ 
E)  No Solution

Question 12

Simplify the following expression algebraically. $2 \cos \left( \frac { 3 \pi } { 2 } - x \right)$

Accepted Answer

A)  $- 2 \cos x$ 
B)  $2 \sin x$ 
C)  $- \frac { 3 } { 2 } \sin x$ 
D)  $- 2 \sin x$ 
E)  $\frac { 3 } { 2 } \sin x$ 
A)  $- 2 \cos x$ 
B)  $2 \sin x$ 
C)  $- \frac { 3 } { 2 } \sin x$ 
D)  $- 2 \sin x$ 
E)  $\frac { 3 } { 2 } \sin x$

Question 13

Use the low of Cosines to solve the given triangle. Round your answer to two decimal places. $a = 1.52 , b = 0.85 , c = 1.35$

Accepted Answer

A)  $A \approx 33.8 ^ { \circ } , B \approx 84.13 ^ { \circ } , C \approx 62.07 ^ { \circ }$ 
B)  $A \approx 62.07 ^ { \circ } , B \approx 33.8 ^ { \circ } , C \approx 84.13 ^ { \circ }$ 
C)  $A \approx 84.13 ^ { \circ } , B \approx 33.8 ^ { \circ } , C \approx 62.07 ^ { \circ }$ 
D)  $A \approx 84.13 ^ { \circ } , B \approx 62.07 ^ { \circ } , C \approx 33.8 ^ { \circ }$ 
E)  $A \approx 62.07 ^ { \circ } , B \approx 84.13 ^ { \circ } , C \approx 33.8 ^ { \circ }$ 
A)  $A \approx 33.8 ^ { \circ } , B \approx 84.13 ^ { \circ } , C \approx 62.07 ^ { \circ }$ 
B)  $A \approx 62.07 ^ { \circ } , B \approx 33.8 ^ { \circ } , C \approx 84.13 ^ { \circ }$ 
C)  $A \approx 84.13 ^ { \circ } , B \approx 33.8 ^ { \circ } , C \approx 62.07 ^ { \circ }$ 
D)  $A \approx 84.13 ^ { \circ } , B \approx 62.07 ^ { \circ } , C \approx 33.8 ^ { \circ }$ 
E)  $A \approx 62.07 ^ { \circ } , B \approx 84.13 ^ { \circ } , C \approx 33.8 ^ { \circ }$

Question 14

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval $[ 0,2 \pi )$ . $\cos ^ { 2 } x - 5 \sin x + 5 = 0$

Accepted Answer

A)  $x = \frac { \pi } { 2 }$ 
B)  $x = \frac { \pi } { 6 } , \frac { 3 \pi } { 2 }$ 
C)  $x = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
D)  solution does not exist 
E)  $x = \frac { 3 \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
A)  $x = \frac { \pi } { 2 }$ 
B)  $x = \frac { \pi } { 6 } , \frac { 3 \pi } { 2 }$ 
C)  $x = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
D)  solution does not exist 
E)  $x = \frac { 3 \pi } { 4 } , \frac { 7 \pi } { 4 }$

Question 15

Use the cofunction identities to evaluate the expression without using a calculator. $$\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29$$

Accepted Answer

A)  $- 2$ 
B)  3 
C)  $- 1$ 
D)  1 
E)  2 
A)  $- 2$ 
B)  3 
C)  $- 1$ 
D)  1 
E)  2

Question 16

Use a graphing utility to select the correct graph $y _ { 1 } \text { and } y _ { 2 }$ in the same viewing window. Use the graphs to determine whether $y _ { 1 } = y _ { 2 }$ . 
Explain your reasoning. 
$y _ { 1 } = \cos ( x + 6 ) , y _ { 2 } = \cos x + \cos 6$

Accepted Answer

A) 
 
No, $y _ { 1 } \neq y _ { 2 }$ because their graphs are different. 
B) 
 
No, $y _ { 1 } \neq y _ { 2 }$ because their graphs are Same. 
C) 
 
Yes, $y _ { 1 } = y _ { 2 }$ because their graphs are different. 
D) 
 
Yes, $y _ { 1 } = y _ { 2 }$ because their graphs are 
same. 
E) 
 
No, $y _ { 1 } = y _ { 2 }$ because their graphs are
 different. 
A) 
 
No, $y _ { 1 } \neq y _ { 2 }$ because their graphs are different. 
B) 
 
No, $y _ { 1 } \neq y _ { 2 }$ because their graphs are Same. 
C) 
 
Yes, $y _ { 1 } = y _ { 2 }$ because their graphs are different. 
D) 
 
Yes, $y _ { 1 } = y _ { 2 }$ because their graphs are 
same. 
E) 
 
No, $y _ { 1 } = y _ { 2 }$ because their graphs are
 different.

Question 17

Use the figure to find the exact value of the trigonometric function.

Accepted Answer

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

Question 18

Use the Law of Sines to solve (if possible) for $c$ . Round your answers to two decimal places. $A = 110 ^ { \circ } , a = 125 , b = 100$

Accepted Answer

A)  $c \approx 48.23$ 
B)  $c \approx 68.23$ 
C)  $c \approx 38.23$ 
D)  $c \approx 58.23$ 
E)  No solution 
A)  $c \approx 48.23$ 
B)  $c \approx 68.23$ 
C)  $c \approx 38.23$ 
D)  $c \approx 58.23$ 
E)  No solution

Question 19

Use the sum-to-product formulas to select the sum or difference as a product. $$\sin 7 \theta + \sin 5 \theta$$

Accepted Answer

A)  $2 \cos 6 \theta \cos \theta$ 
B)  $2 \sin 7 \theta \cos 5 \theta$ 
C)  $2 \sin 6 \theta \sin \theta$ 
D)  $2 \cos 6 \theta \sin \theta$ 
E)  $2 \sin 6 \theta \cos \theta$ 
A)  $2 \cos 6 \theta \cos \theta$ 
B)  $2 \sin 7 \theta \cos 5 \theta$ 
C)  $2 \sin 6 \theta \sin \theta$ 
D)  $2 \cos 6 \theta \sin \theta$ 
E)  $2 \sin 6 \theta \cos \theta$

Question 20

Use the Law of Sines to solve (if possible) for $c$ . Round your answers to two decimal places. $$A = 110 ^ { \circ } , a = 250 , b = 200$$

Accepted Answer

A)  $c \approx 86.46$ 
B)  $ c \approx 96.46$ 
C)  $c \approx 106.46$ 
D)  $c \approx 116.46$ 
E)  No solution 
A)  $c \approx 86.46$ 
B)  $ c \approx 96.46$ 
C)  $c \approx 106.46$ 
D)  $c \approx 116.46$ 
E)  No solution

Solve the following equation. $4 \sin ^ { 2 } x = 12 \cos ^ { 2 } x$

Given $a = 9 , b = 11 , \text { and } c = 6$ , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places. $Given a = 9 , b = 11 , \text { and } c = 6 , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.$

Find the rate of change of the function $f ( x ) = - x + \sin x$

Use the half-angle formulas to determine the exact value of the given trigonometric expression. $\tan \frac { 3 \pi } { 8 }$

Use the given values to evaluate (if possible) three trigonometric functions cosec $\theta$ $\tan \theta , \cos \theta$ $\sin \theta = - 4 , \quad \cot \theta = 0$

Use the sum-to-product formulas to select the sum or difference as a product. $\cos 3 \theta + \cos 6 \theta$

Evaluate the following expression. $\frac { 3 + 3 \sin 3 \theta } { \cos 3 \theta } + \frac { 3 \cos 3 \theta } { 1 + \sin 3 \theta }$

Evaluate the expression. $\cos 10 \alpha$

Use a double-angle formula to rewrite the expression. $6 \sin ^ { 2 } x - 3$

Use the Law of Sines to solve (if possible) the triangle. Round your answers to two decimal places. $A = 76 ^ { \circ } , a = 102 , b = 63$

Simplify the following expression algebraically. $2 \cos \left( \frac { 3 \pi } { 2 } - x \right)$

Use the low of Cosines to solve the given triangle. Round your answer to two decimal places. $a = 1.52 , b = 0.85 , c = 1.35$

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval $[ 0,2 \pi )$ . $\cos ^ { 2 } x - 5 \sin x + 5 = 0$

Use the cofunction identities to evaluate the expression without using a calculator. $\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29$

Use a graphing utility to select the correct graph $y _ { 1 } \text { and } y _ { 2 }$ in the same viewing window. Use the graphs to determine whether $y _ { 1 } = y _ { 2 }$ . Explain your reasoning. $y _ { 1 } = \cos ( x + 6 ) , y _ { 2 } = \cos x + \cos 6$

Use the figure to find the exact value of the trigonometric function.

Use the Law of Sines to solve (if possible) for $c$ . Round your answers to two decimal places. $A = 110 ^ { \circ } , a = 125 , b = 100$

Use the sum-to-product formulas to select the sum or difference as a product. $\sin 7 \theta + \sin 5 \theta$

Use the Law of Sines to solve (if possible) for $c$ . Round your answers to two decimal places. $A = 110 ^ { \circ } , a = 250 , b = 200$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Topics in Analytic Geometry

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Exam 5: Analytic Trigonometry

Solve the following equation. 4sin⁡2x=12cos⁡2x4 \sin ^ { 2 } x = 12 \cos ^ { 2 } x4sin2x=12cos2x

Given a=9,b=11, and c=6a = 9 , b = 11 , \text { and } c = 6a=9,b=11, and c=6 , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.

Find the rate of change of the function f(x)=−x+sin⁡xf ( x ) = - x + \sin xf(x)=−x+sinx

Use the half-angle formulas to determine the exact value of the given trigonometric expression. tan⁡3π8\tan \frac { 3 \pi } { 8 }tan83π​

Use the given values to evaluate (if possible) three trigonometric functions cosec θ\thetaθ tan⁡θ,cos⁡θ\tan \theta , \cos \thetatanθ,cosθ sin⁡θ=−4,cot⁡θ=0\sin \theta = - 4 , \quad \cot \theta = 0sinθ=−4,cotθ=0

Use the sum-to-product formulas to select the sum or difference as a product. cos⁡3θ+cos⁡6θ\cos 3 \theta + \cos 6 \thetacos3θ+cos6θ

Evaluate the following expression. 3+3sin⁡3θcos⁡3θ+3cos⁡3θ1+sin⁡3θ\frac { 3 + 3 \sin 3 \theta } { \cos 3 \theta } + \frac { 3 \cos 3 \theta } { 1 + \sin 3 \theta }cos3θ3+3sin3θ​+1+sin3θ3cos3θ​

Evaluate the expression. cos⁡10α\cos 10 \alphacos10α

Use a double-angle formula to rewrite the expression. 6sin⁡2x−36 \sin ^ { 2 } x - 36sin2x−3

Use the Law of Sines to solve (if possible) the triangle. Round your answers to two decimal places. A=76∘,a=102,b=63A = 76 ^ { \circ } , a = 102 , b = 63A=76∘,a=102,b=63

Simplify the following expression algebraically. 2cos⁡(3π2−x)2 \cos \left( \frac { 3 \pi } { 2 } - x \right)2cos(23π​−x)

Use the low of Cosines to solve the given triangle. Round your answer to two decimal places. a=1.52,b=0.85,c=1.35a = 1.52 , b = 0.85 , c = 1.35a=1.52,b=0.85,c=1.35

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval [0,2π)[ 0,2 \pi )[0,2π) . cos⁡2x−5sin⁡x+5=0\cos ^ { 2 } x - 5 \sin x + 5 = 0cos2x−5sinx+5=0

Use the cofunction identities to evaluate the expression without using a calculator. tan⁡261+cot⁡218−sec⁡272−csc⁡229\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29tan261+cot218−sec272−csc229

Use the figure to find the exact value of the trigonometric function.

Use the Law of Sines to solve (if possible) for ccc . Round your answers to two decimal places. A=110∘,a=125,b=100A = 110 ^ { \circ } , a = 125 , b = 100A=110∘,a=125,b=100

Use the sum-to-product formulas to select the sum or difference as a product. sin⁡7θ+sin⁡5θ\sin 7 \theta + \sin 5 \thetasin7θ+sin5θ

Use the Law of Sines to solve (if possible) for ccc . Round your answers to two decimal places. A=110∘,a=250,b=200A = 110 ^ { \circ } , a = 250 , b = 200A=110∘,a=250,b=200

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Topics in Analytic Geometry

Filters

Solve the following equation. $4 \sin ^ { 2 } x = 12 \cos ^ { 2 } x$

Given $a = 9 , b = 11 , \text { and } c = 6$ , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places. $Given a = 9 , b = 11 , \text { and } c = 6 , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.$

Find the rate of change of the function $f ( x ) = - x + \sin x$

Use the half-angle formulas to determine the exact value of the given trigonometric expression. $\tan \frac { 3 \pi } { 8 }$

Use the given values to evaluate (if possible) three trigonometric functions cosec $\theta$ $\tan \theta , \cos \theta$ $\sin \theta = - 4 , \quad \cot \theta = 0$

Use the sum-to-product formulas to select the sum or difference as a product. $\cos 3 \theta + \cos 6 \theta$

Evaluate the following expression. $\frac { 3 + 3 \sin 3 \theta } { \cos 3 \theta } + \frac { 3 \cos 3 \theta } { 1 + \sin 3 \theta }$

Evaluate the expression. $\cos 10 \alpha$

Use a double-angle formula to rewrite the expression. $6 \sin ^ { 2 } x - 3$

Use the Law of Sines to solve (if possible) the triangle. Round your answers to two decimal places. $A = 76 ^ { \circ } , a = 102 , b = 63$

Simplify the following expression algebraically. $2 \cos \left( \frac { 3 \pi } { 2 } - x \right)$

Use the low of Cosines to solve the given triangle. Round your answer to two decimal places. $a = 1.52 , b = 0.85 , c = 1.35$

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval $[ 0,2 \pi )$ . $\cos ^ { 2 } x - 5 \sin x + 5 = 0$

Use the cofunction identities to evaluate the expression without using a calculator. $\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29$

Use the Law of Sines to solve (if possible) for $c$ . Round your answers to two decimal places. $A = 110 ^ { \circ } , a = 125 , b = 100$

Use the sum-to-product formulas to select the sum or difference as a product. $\sin 7 \theta + \sin 5 \theta$

Use the Law of Sines to solve (if possible) for $c$ . Round your answers to two decimal places. $A = 110 ^ { \circ } , a = 250 , b = 200$