Question 1

Find the expression as the sine or cosine of an angle. $$\cos 9 x \cos 8 y + \sin 9 x \sin 8 y$$

Accepted Answer

A)  $\cos ( 9 x + 8 y )$ 
B)  $\cos ( 8 x - 9 y )$ 
C)  $\cos ( 9 x - 8 y )$ 
D)  $\sin ( 9 x - 8 y )$ 
E)  $\sin ( 8 x - 9 y )$ 
A)  $\cos ( 9 x + 8 y )$ 
B)  $\cos ( 8 x - 9 y )$ 
C)  $\cos ( 9 x - 8 y )$ 
D)  $\sin ( 9 x - 8 y )$ 
E)  $\sin ( 8 x - 9 y )$ C

Question 2

Given $a = 9 , b = 12 , \text { and } c = 7 ,$ , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Accepted Answer

A) $96.38 ^ { \circ }$ 
B)  $48.19 ^ { \circ }$ 
C)  $35.43 ^ { \circ }$ 
D)  $80.44 ^ { \circ }$ 
E)  $60.33 ^ { \circ }$ 
A) $96.38 ^ { \circ }$ 
B)  $48.19 ^ { \circ }$ 
C)  $35.43 ^ { \circ }$ 
D)  $80.44 ^ { \circ }$ 
E)  $60.33 ^ { \circ }$ A

Question 3

Evaluate the following expression. $$( 1 + \sin \alpha ) ( 1 - \sin \alpha )$$

Accepted Answer

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

Question 4

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. Round your answer to two decimal places. 
$a = 154 , B = 10 ^ { \circ } , C = 5 ^ { \circ }$

Accepted Answer

A)  Law of Cosines; No solution 
B)  Law of Sines; $A = 165 ^ { \circ } , b \approx 51.86 , c \approx 103.32$ 
C)  Law of Sines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$ 
D)  Law of Cosines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$ 
E)  Law of Sines; No solution 
A)  Law of Cosines; No solution 
B)  Law of Sines; $A = 165 ^ { \circ } , b \approx 51.86 , c \approx 103.32$ 
C)  Law of Sines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$ 
D)  Law of Cosines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$ 
E)  Law of Sines; No solution

Question 5

Perform the multiplication and use the fundamental identities to simplify. 
$( \sin x + \cos x ) ^ { 2 }$

Accepted Answer

A)  $1 + \sin x + \cos x$ 
B)  $1 + \sin x \cos x$ 
C)  $1 + 2 \sin x + \cos x$ 
D)  $1 + 2 \sin x \cos x$ 
E)  $2 + 2 \sin x \cos x$ 
A)  $1 + \sin x + \cos x$ 
B)  $1 + \sin x \cos x$ 
C)  $1 + 2 \sin x + \cos x$ 
D)  $1 + 2 \sin x \cos x$ 
E)  $2 + 2 \sin x \cos x$

Question 6

Evaluate the expression. $\tan \frac { a } { 2 }$

Accepted Answer

A)  $\cos a + \cot a$ 
B)  $\cos a - \cot a$ 
C)  $\csc a - \cot a$ 
D)  $\csc a - \tan a$ 
E)  $\csc a + \cot a$ 
A)  $\cos a + \cot a$ 
B)  $\cos a - \cot a$ 
C)  $\csc a - \cot a$ 
D)  $\csc a - \tan a$ 
E)  $\csc a + \cot a$

Question 7

Find all solutions of the following equation in the interval 
$[ 0,2 \pi )$ . $\sin x - 2 = \cos x - 2$

Accepted Answer

A)  $\frac { \pi } { 4 } , \frac { 5 \pi } { 4 }$ 
B)  $\frac { \pi } { 2 } , \frac { 5 \pi } { 2 }$ 
C)  $\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 }$. 
D)  $\frac { 3 \pi } { 4 } , \frac { 7 \pi } { 4 }$. 
E)  $\frac { \pi } { 2 } , \frac { 5 \pi } { 2 }$. 
A)  $\frac { \pi } { 4 } , \frac { 5 \pi } { 4 }$ 
B)  $\frac { \pi } { 2 } , \frac { 5 \pi } { 2 }$ 
C)  $\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 }$. 
D)  $\frac { 3 \pi } { 4 } , \frac { 7 \pi } { 4 }$. 
E)  $\frac { \pi } { 2 } , \frac { 5 \pi } { 2 }$.

Question 8

Use a graphing utility to graph the function.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 9

Solve the following equation. $9 \sec ^ { 2 } x - 12 = 0$

Accepted Answer

A) $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
B) $\frac { \pi } { 6 } + n \pi , \frac { 5 \pi } { 6 } + n \pi$ 
C)  $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
D)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
E)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
A) $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
B) $\frac { \pi } { 6 } + n \pi , \frac { 5 \pi } { 6 } + n \pi$ 
C)  $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
D)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
E)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$

Question 10

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx. $\sin x = \frac { 1 } { 2 }$

Accepted Answer

A) 
$\begin{array} { l } 
\cos x = \frac { \sqrt { 3 } } { 2 } \
\csc x = 2 \
\tan x = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
B) 
$\begin{array} { l } 
\cos x = - \frac { \sqrt { 3 } } { 2 } \
\csc x = - 2 \
\tan x = - \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
C) 
$\begin{array} { l } 
\cos x = - \frac { \sqrt { 3 } } { 2 } \
\csc x = 2 \
\tan x = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
D) 
$\begin{array} { l } 
\cos x = \frac { \sqrt { 3 } } { 2 } \
\csc x = \frac { 1 } { 2 }
\end{array}$
$\tan x = \frac { \sqrt { 3 } } { 3 }$ 
E) 
$\begin{array} { l } 
\cos x = \frac { \sqrt { 3 } } { 2 } \
\csc x = 2 \
\tan x = - \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
A) 
$\begin{array} { l } 
\cos x = \frac { \sqrt { 3 } } { 2 } \
\csc x = 2 \
\tan x = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
B) 
$\begin{array} { l } 
\cos x = - \frac { \sqrt { 3 } } { 2 } \
\csc x = - 2 \
\tan x = - \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
C) 
$\begin{array} { l } 
\cos x = - \frac { \sqrt { 3 } } { 2 } \
\csc x = 2 \
\tan x = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
D) 
$\begin{array} { l } 
\cos x = \frac { \sqrt { 3 } } { 2 } \
\csc x = \frac { 1 } { 2 }
\end{array}$
$\tan x = \frac { \sqrt { 3 } } { 3 }$ 
E) 
$\begin{array} { l } 
\cos x = \frac { \sqrt { 3 } } { 2 } \
\csc x = 2 \
\tan x = - \frac { \sqrt { 3 } } { 3 }
\end{array}$

Question 11

Use the trigonometric substitution to select the algebraic expression as a trigonomet- ric function of $\theta$ , where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } .$ . Then find $\sin \theta \text { and } \cos \theta$ $2 = \sqrt { 4 - x ^ { 2 } } , x = 2 \sin \theta$

Accepted Answer

A)  $2 \cos \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$ 
B)  $2 \sin \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$ 
C)  $2 \cos \theta = 2 ; \sin \theta = 1 ; \cos \theta = 0$ 
D)  $4 \sin \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$ 
E)  $4 \cos \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$ 
A)  $2 \cos \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$ 
B)  $2 \sin \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$ 
C)  $2 \cos \theta = 2 ; \sin \theta = 1 ; \cos \theta = 0$ 
D)  $4 \sin \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$ 
E)  $4 \cos \theta = 2 ; \sin \theta = 0 ; \cos \theta = 1$

Question 12

Use the formula $\operatorname { asin } B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ where $\bar { C } = \arctan ( b / a ) , a > 0$ to find the trigonometric expression in the following forms. 
$\begin{array} { l } 
y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C ) \
2 \sin \theta + 7 \cos \theta
\end{array}$

Accepted Answer

A)  $\sqrt { 53 } \sin ( \theta + 1.2925 )$ 
B)  $\sqrt { 53 } \sin ( \theta - 1.2925 )$ 
C)  $2 \sin ( \theta + 1.2925 )$ 
D)  $7 \sin ( \theta + 1.2925 )$ 
E)  $\sin ( \theta + 1.2925 )$ 
A)  $\sqrt { 53 } \sin ( \theta + 1.2925 )$ 
B)  $\sqrt { 53 } \sin ( \theta - 1.2925 )$ 
C)  $2 \sin ( \theta + 1.2925 )$ 
D)  $7 \sin ( \theta + 1.2925 )$ 
E)  $\sin ( \theta + 1.2925 )$

Question 13

Use the cofunction identities to evaluate the expression without using a calculator. $\tan ^ { 2 } 71 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 19$

Accepted Answer

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

Question 14

Use the given values to evaluate (if possible) three trigonometric functions sinx, cosx, cotx. $\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }$

Accepted Answer

A) 
$\begin{array} { l } 
\sin x = \frac { 25 } { 24 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
B) 
$\begin{array} { l } 
\sin x = \frac { 25 } { 7 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
C) 
$\begin{array} { l } 
\sin x = \frac { 24 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
D) 
$\begin{array} { l } 
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
E) 
$\begin{array} { l } 
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
A) 
$\begin{array} { l } 
\sin x = \frac { 25 } { 24 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
B) 
$\begin{array} { l } 
\sin x = \frac { 25 } { 7 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
C) 
$\begin{array} { l } 
\sin x = \frac { 24 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
D) 
$\begin{array} { l } 
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 24 } { 7 } \
\cos x = \frac { 24 } { 25 }
\end{array}$ 
E) 
$\begin{array} { l } 
\sin x = \frac { 7 } { 25 } \
\cot x = \frac { 7 } { 24 } \
\cos x = \frac { 24 } { 25 }
\end{array}$

Question 15

Solve the following equation. $$6 \sec ^ { 2 } x - 8 = 0$$

Accepted Answer

A)  $\frac { \pi } { 6 } + n \pi , \frac { 5 \pi } { 6 } + n \pi$ 
B)  $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
C)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
D)  $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
E)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
A)  $\frac { \pi } { 6 } + n \pi , \frac { 5 \pi } { 6 } + n \pi$ 
B)  $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
C)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
D)  $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
E)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$

Question 16

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). $y = \frac { 1 } { 4 } \sin 2 t + \frac { 1 } { 3 } \cos 2 t$ 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)  $\quad y = \sin ( 2 t - 0.9273 )$ 
B)  $y = \sin ( 2 t + 0.9273 )$ 
C)  $y = \frac { 12 } { 5 } \sin ( 2 t - 0.9273 )$ 
D)  $y = \frac { 5 } { 12 } \sin ( 2 t + 0.9273 )$ 
E)  $y = \frac { 12 } { 5 } \sin ( 2 t + 0.9273 )$ 
A)  $\quad y = \sin ( 2 t - 0.9273 )$ 
B)  $y = \sin ( 2 t + 0.9273 )$ 
C)  $y = \frac { 12 } { 5 } \sin ( 2 t - 0.9273 )$ 
D)  $y = \frac { 5 } { 12 } \sin ( 2 t + 0.9273 )$ 
E)  $y = \frac { 12 } { 5 } \sin ( 2 t + 0.9273 )$

Question 17

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places. $$a = 13 , b = 17 , c = 23$$

Accepted Answer

A)  $A \approx 33.92 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 99.24 ^ { \circ }$ 
B)  $A \approx 46.84 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 86.32 ^ { \circ }$ 
C)  $A \approx 33.92 ^ { \circ } , B \approx 99.24 ^ { \circ } , C \approx 46.84 ^ { \circ }$ 
D)  $A \approx 99.24 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 33.92 ^ { \circ }$ 
E)  $A \approx 46.84 ^ { \circ } , B \approx 33.92 ^ { \circ } , C \approx 99.24 ^ { \circ }$ 
A)  $A \approx 33.92 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 99.24 ^ { \circ }$ 
B)  $A \approx 46.84 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 86.32 ^ { \circ }$ 
C)  $A \approx 33.92 ^ { \circ } , B \approx 99.24 ^ { \circ } , C \approx 46.84 ^ { \circ }$ 
D)  $A \approx 99.24 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 33.92 ^ { \circ }$ 
E)  $A \approx 46.84 ^ { \circ } , B \approx 33.92 ^ { \circ } , C \approx 99.24 ^ { \circ }$

Question 18

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ $4 \sin x + \csc x = 0$

Accepted Answer

A)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
B)  No solution 
C)  $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
D)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
E)  $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
A)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
B)  No solution 
C)  $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
D)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
E)  $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$

Question 19

Use a calculator to calculate the value of $\theta$ from the given identity. $\sin ( - \theta ) = - \sin \theta , \theta = 255 ^ { \circ }$

Accepted Answer

A)  $\sin ( - 255 ) = - \sin 255 \approx - 0.9659$ 
B)  $\sin ( - 255 ) = - \sin 255 \approx 0.9959$ 
C)  $\sin ( - 255 ) = - \sin 255 \approx 0.9859$ 
D)  $\sin ( - 255 ) = - \sin 255 \approx - 0.9859$ 
E)  $\sin (-255)=-\sin 255 \approx 0.9659$ 
A)  $\sin ( - 255 ) = - \sin 255 \approx - 0.9659$ 
B)  $\sin ( - 255 ) = - \sin 255 \approx 0.9959$ 
C)  $\sin ( - 255 ) = - \sin 255 \approx 0.9859$ 
D)  $\sin ( - 255 ) = - \sin 255 \approx - 0.9859$ 
E)  $\sin (-255)=-\sin 255 \approx 0.9659$

Question 20

Use a calculator to calculate the value of $\theta$ from the given identity. $\sin ( - \theta ) = - \sin \theta , \theta = 251 ^ { \circ }$

Accepted Answer

A)  $ \sin ( - 251 ) = - \sin 251 \approx 0.9755$ 
B)  $\sin ( - 251 ) = - \sin 251 \approx 0.9455$ 
C)  $ \sin ( - 251 ) = - \sin 251 \approx - 0.9455$ 
D)  $\sin ( - 251 ) = - \sin 251 \approx - 0.9655$ 
E) $\sin (-251)=-\sin 251 \approx 0.9655$ 
A)  $ \sin ( - 251 ) = - \sin 251 \approx 0.9755$ 
B)  $\sin ( - 251 ) = - \sin 251 \approx 0.9455$ 
C)  $ \sin ( - 251 ) = - \sin 251 \approx - 0.9455$ 
D)  $\sin ( - 251 ) = - \sin 251 \approx - 0.9655$ 
E) $\sin (-251)=-\sin 251 \approx 0.9655$

Find the expression as the sine or cosine of an angle. $\cos 9 x \cos 8 y + \sin 9 x \sin 8 y$

Given $a = 9 , b = 12 , \text { and } c = 7 ,$ , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Evaluate the following expression. $( 1 + \sin \alpha ) ( 1 - \sin \alpha )$

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. Round your answer to two decimal places. $a = 154 , B = 10 ^ { \circ } , C = 5 ^ { \circ }$

Perform the multiplication and use the fundamental identities to simplify. $( \sin x + \cos x ) ^ { 2 }$

Evaluate the expression. $\tan \frac { a } { 2 }$

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ . $\sin x - 2 = \cos x - 2$

Use a graphing utility to graph the function.

Solve the following equation. $9 \sec ^ { 2 } x - 12 = 0$

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx. $\sin x = \frac { 1 } { 2 }$

Use the trigonometric substitution to select the algebraic expression as a trigonomet- ric function of $\theta$ , where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } .$ . Then find $\sin \theta \text { and } \cos \theta$ $2 = \sqrt { 4 - x ^ { 2 } } , x = 2 \sin \theta$

Use the formula $\operatorname { asin } B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ where $\bar { C } = \arctan ( b / a ) , a > 0$ to find the trigonometric expression in the following forms. y=(B\theta+C) 2\theta+7\theta

Use the cofunction identities to evaluate the expression without using a calculator. $\tan ^ { 2 } 71 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 19$

Use the given values to evaluate (if possible) three trigonometric functions sinx, cosx, cotx. $\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }$

Solve the following equation. $6 \sec ^ { 2 } x - 8 = 0$

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places. $a = 13 , b = 17 , c = 23$

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ $4 \sin x + \csc x = 0$

Use a calculator to calculate the value of $\theta$ from the given identity. $\sin ( - \theta ) = - \sin \theta , \theta = 255 ^ { \circ }$

Use a calculator to calculate the value of $\theta$ from the given identity. $\sin ( - \theta ) = - \sin \theta , \theta = 251 ^ { \circ }$

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Exam 5: Analytic Trigonometry

Find the expression as the sine or cosine of an angle. cos⁡9xcos⁡8y+sin⁡9xsin⁡8y\cos 9 x \cos 8 y + \sin 9 x \sin 8 ycos9xcos8y+sin9xsin8y

Given a=9,b=12, and c=7,a = 9 , b = 12 , \text { and } c = 7 ,a=9,b=12, and c=7, , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Evaluate the following expression. (1+sin⁡α)(1−sin⁡α)( 1 + \sin \alpha ) ( 1 - \sin \alpha )(1+sinα)(1−sinα)

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. Round your answer to two decimal places. a=154,B=10∘,C=5∘a = 154 , B = 10 ^ { \circ } , C = 5 ^ { \circ }a=154,B=10∘,C=5∘

Perform the multiplication and use the fundamental identities to simplify. (sin⁡x+cos⁡x)2( \sin x + \cos x ) ^ { 2 }(sinx+cosx)2

Evaluate the expression. tan⁡a2\tan \frac { a } { 2 }tan2a​

Find all solutions of the following equation in the interval [0,2π)[ 0,2 \pi )[0,2π) . sin⁡x−2=cos⁡x−2\sin x - 2 = \cos x - 2sinx−2=cosx−2

Use a graphing utility to graph the function.

Solve the following equation. 9sec⁡2x−12=09 \sec ^ { 2 } x - 12 = 09sec2x−12=0

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx. sin⁡x=12\sin x = \frac { 1 } { 2 }sinx=21​

Use the cofunction identities to evaluate the expression without using a calculator. tan⁡271+cot⁡218−sec⁡272−csc⁡219\tan ^ { 2 } 71 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 19tan271+cot218−sec272−csc219

Use the given values to evaluate (if possible) three trigonometric functions sinx, cosx, cotx. csc⁡x=257,tan⁡x=724\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }cscx=725​,tanx=247​

Solve the following equation. 6sec⁡2x−8=06 \sec ^ { 2 } x - 8 = 06sec2x−8=0

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places. a=13,b=17,c=23a = 13 , b = 17 , c = 23a=13,b=17,c=23

Find all solutions of the following equation in the interval [0,2π)[ 0,2 \pi )[0,2π) 4sin⁡x+csc⁡x=04 \sin x + \csc x = 04sinx+cscx=0

Use a calculator to calculate the value of θ\thetaθ from the given identity. sin⁡(−θ)=−sin⁡θ,θ=255∘\sin ( - \theta ) = - \sin \theta , \theta = 255 ^ { \circ }sin(−θ)=−sinθ,θ=255∘

Use a calculator to calculate the value of θ\thetaθ from the given identity. sin⁡(−θ)=−sin⁡θ,θ=251∘\sin ( - \theta ) = - \sin \theta , \theta = 251 ^ { \circ }sin(−θ)=−sinθ,θ=251∘

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Find the expression as the sine or cosine of an angle. $\cos 9 x \cos 8 y + \sin 9 x \sin 8 y$

Given $a = 9 , b = 12 , \text { and } c = 7 ,$ , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Evaluate the following expression. $( 1 + \sin \alpha ) ( 1 - \sin \alpha )$

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. Round your answer to two decimal places. $a = 154 , B = 10 ^ { \circ } , C = 5 ^ { \circ }$

Perform the multiplication and use the fundamental identities to simplify. $( \sin x + \cos x ) ^ { 2 }$

Evaluate the expression. $\tan \frac { a } { 2 }$

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ . $\sin x - 2 = \cos x - 2$

Solve the following equation. $9 \sec ^ { 2 } x - 12 = 0$

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx. $\sin x = \frac { 1 } { 2 }$

Use the cofunction identities to evaluate the expression without using a calculator. $\tan ^ { 2 } 71 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 19$

Use the given values to evaluate (if possible) three trigonometric functions sinx, cosx, cotx. $\csc x = \frac { 25 } { 7 } , \tan x = \frac { 7 } { 24 }$

Solve the following equation. $6 \sec ^ { 2 } x - 8 = 0$

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places. $a = 13 , b = 17 , c = 23$

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ $4 \sin x + \csc x = 0$

Use a calculator to calculate the value of $\theta$ from the given identity. $\sin ( - \theta ) = - \sin \theta , \theta = 255 ^ { \circ }$

Use a calculator to calculate the value of $\theta$ from the given identity. $\sin ( - \theta ) = - \sin \theta , \theta = 251 ^ { \circ }$