Deck 6: Analytic Trigonometry

Question 1

Find the exact value of the expression.

- $\sin ^ { - 1 } ( 0.5 )$

A) $\frac { \pi } { 6 }$
B) $\frac { 7 \pi } { 3 }$
C) $\frac { \pi } { 3 }$
D) $\frac { 7 \pi } { 6 }$

Answer 1

$\frac { \pi } { 6 }$

Question 2

Use a calculator to find the value of the expression rounded to two decimal places.

- $\sin ^ { - 1 } ( 0.7 )$

A) 44.43
B) 0.78
C) 45.57
D) 0.80

Answer 2

0.78

Question 3

Find the exact value of the expression.

- $$\tan ^ { - 1 } \frac { \sqrt { 3 } } { 3 }$$

A) $\frac { \pi } { 6 }$
B) $\frac { \pi } { 4 }$
C) $\frac { \pi } { 3 }$
D) $\frac { 7 \pi } { 6 }$

Answer 3

$\frac { \pi } { 6 }$

Question 4

Find the exact value of the expression. Do not use a calculator.

- $\tan \left[ \tan ^ { - 1 } ( - 0.4 ) \right]$

A) -0.6
B) -0.4
C) -2.3652
D) -2.5

Question 5

Find the exact value of the expression. Do not use a calculator.

- $\sin \left[ \sin ^ { - 1 } ( - 0.3 ) \right]$

A) 2.7
B) -2.7
C) 0.3
D) -0.3

Question 6

Find the exact value of the expression.

- $$\sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 }$$

A) $\frac { 3 \pi } { 4 }$
B) $\frac { 2 \pi } { 3 }$
C) $\frac { \pi } { 4 }$
D) $\frac { \pi } { 3 }$

Question 7

Find the exact value of the expression.

- $$\cos ^ { - 1 } \frac { \sqrt { 3 } } { 2 }$$

A) $\frac { 7 \pi } { 4 }$
B) $\frac { \pi } { 4 }$
C) $\frac { 11 \pi } { 6 }$
D) $\frac { \pi } { 6 }$

Question 8

Use a calculator to find the value of the expression rounded to two decimal places.

- $\sin ^ { - 1 } \left( \frac { \sqrt { 5 } } { 5 } \right)$

A) 63.44
B) 1.11
C) 26.57
D) 0.46

Question 9

Use a calculator to find the value of the expression rounded to two decimal places.

- $\cos ^ { - 1 } \left( - \frac { 4 } { 5 } \right)$

A) -0.93
B) 143.13
C) 2.50
D) -53.13

Question 10

Find the exact value of the expression. Do not use a calculator.

- $\cos ^ { - 1 } \left[ \cos \left( - \frac { 3 \pi } { 5 } \right) \right]$

A) $- \frac { 3 \pi } { 5 }$
B) $\frac { 2 \pi } { 5 }$
C) $\frac { 3 \pi } { 5 }$
D) $- \frac { 2 \pi } { 5 }$

Question 11

Find the exact value of the expression.

- $\tan ^ { - 1 } ( 1 )$

A) $\frac { \pi } { 4 }$
B) $\frac { 5 \pi } { 4 }$
C) $\frac { 3 \pi } { 4 }$
D) $\frac { 7 \pi } { 4 }$

Question 12

Find the exact value of the expression. Do not use a calculator.

- $$\tan ^ { - 1 } \left[ \tan \left( \frac { 6 \pi } { 7 } \right) \right]$$

A) $- \frac { 6 \pi } { 7 }$
B) $\frac { \pi } { 7 }$
C) $- \frac { \pi } { 7 }$
D) $\frac { 6 \pi } { 7 }$

Question 13

Find the exact value of the expression. Do not use a calculator.

- $\cos \left[ \cos ^ { - 1 } ( - 0.9372 ) \right]$

A) -0.4686
B) -0.9372
C) 0.9372
D) 0.4686

Question 14

Use a calculator to find the value of the expression rounded to two decimal places.

- $\cos ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 3 } \right)$

A) -0.62
B) 125.26
C) 2.19
D) -35.26

Question 15

Use a calculator to find the value of the expression rounded to two decimal places.

- $\sin ^ { - 1 } \left( - \frac { 1 } { 7 } \right)$

A) -8.21
B) -0.14
C) 1.71
D) 98.21

Question 16

Use a calculator to find the value of the expression rounded to two decimal places.

- $\cos ^ { - 1 } ( 0.3 )$

A) 0.30
B) 72.54
C) 1.27
D) 17.46

Question 17

Find the exact value of the expression. Do not use a calculator.

- $$\sin ^ { - 1 } \left[ \sin \left( \frac { 6 \pi } { 7 } \right) \right]$$

A) $\frac { \pi } { 7 }$
B) $\frac { 7 } { 6 \pi }$
C) $\frac { 6 \pi } { 7 }$
D) $\frac { 7 } { \pi }$

Question 18

Find the exact value of the expression.

- $$\cos ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 2 } \right)$$

A) $\frac { 5 \pi } { 6 }$
B) $\frac { \pi } { 3 }$
C) $\frac { \pi } { 6 }$
D) $\frac { 2 \pi } { 3 }$

Question 19

Use a calculator to find the value of the expression rounded to two decimal places.

- $\tan ^ { - 1 } ( 0.2 )$

A) 78.69
B) 11.31
C) 0.20
D) 1.37

Question 20

Find the exact value of the expression. Do not use a calculator.

- $\sin \left[ \sin ^ { - 1 } ( - 0.7 ) \right]$

A) -0.7
B) -1.4286
C) -0.3
D) -1.5523

Question 21

Find the exact value of the expression. Do not use a calculator.

- $$\cos ^ { - 1 } \left[ \cos \left( \frac { \pi } { 10 } \right) \right]$$

A) $\frac { \pi } { 10 }$
B) $10 \pi$
C) $- 10 \pi$
D) $- \frac { \pi } { 10 }$

Question 22

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $$f ( x ) = 5 \tan ( 10 x - 9 )$$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 5 \tan ^ { - 1 } ( 10 \mathrm { x } - 9 )$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 5 } \left[ \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 10 } \right) + 9 \right]$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 10 } \left[ \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 5 } \right) - 9 \right]$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 10 } \left[ \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 5 } \right) + 9 \right]$

Question 23

Find the exact value of the expression. Do not use a calculator.

- $$\tan ^ { - 1 } \left[ \tan \left( - \frac { \pi } { 8 } \right) \right]$$

A) $- 8 \pi$
B) $\frac { \pi } { 8 }$
C) $8 \pi$
D) $- \frac { \pi } { 8 }$

Question 24

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = \tan ( x - 4 ) + 7$$

A) Domain of f: $( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 8 , - 6 ]$

B) Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } + 7 ; k$ an integer
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

C) Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

D) Domain of $\mathrm { f } : [ - 4,4 ]$

Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

Question 25

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = 6 \tan x + 10$$

A) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 4,16 ]$

B) Domain of f: $x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

C) Domain of $\mathrm { f } : ( * , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : \mathrm { x } \neq \frac { ( 2 \mathrm { k } + 1 ) \pi } { 2 } ; \mathrm { k }$ an integer

D) Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer

Domain of $f ^ { - 1 } : [ 4,16 ]$

Question 26

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $$f ( x ) = \cos ( x - 9 ) - 5$$

A) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } ( x - 5 ) - 9$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \cos ^ { - 1 } ( \mathrm { x } + 5 ) + 9$
C) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } ( x + 9 ) + 5$
D) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } ( x - 9 ) - 5$

Question 27

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = 3 \sin ( 5 x )$$

A) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 2,8 ]$

B) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 5,5 ]$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 3,3 ]$

D) Domain of $\mathrm { f } : \left[ - \frac { 1 } { 5 } , \frac { 1 } { 5 } \right]$

Domain of $\mathrm { f } ^ { - 1 } : ( - \infty , \infty )$

Question 28

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $$f ( x ) = - 4 \cos ( 10 x + 7 )$$

A) $f ^ { - 1 } ( x ) = - 4 \cos ^ { - 1 } ( 10 x + 7 )$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 4 } \left[ \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 10 } \right) - 7 \right]$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 10 } \left[ \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 4 } \right) - 7 \right]$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 10 } \left[ \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 4 } \right) + 7 \right]$

Question 29

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = 2 \sin ( 3 x - 1 )$$

A) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 3,3 ]$

B) Domain of f: $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

C) Domain of $f : [ - 2,2 ]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

D) Domain of $\mathrm { f } : ( \infty , \infty )$

Domain of $f ^ { - 1 } : [ - 2,2 ]$

Question 30

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $$f ( x ) = 4 \tan ( 9 x )$$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 4 } \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 9 } \right)$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 4 \tan ( 9 \mathrm { x } ) }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 4 \tan ^ { - 1 } ( 9 \mathrm { x } )$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 9 } \tan ^ { - 1 } \left( \frac { \mathrm { x } } { 4 } \right)$

Question 31

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $$f ( x ) = 7 \cos x + 4$$

A) $f ^ { - 1 } ( x ) = 7 \cos ^ { - 1 } x + 4$
B) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } \left( \frac { x + 4 } { 7 } \right)$
C) $f ^ { - 1 } ( x ) = \sin \left( \frac { x - 4 } { 7 } \right)$
D) $f ^ { - 1 } ( x ) = \cos ^ { - 1 } \left( \frac { x - 4 } { 7 } \right)$

Question 32

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = - 5 \cos ( 9 x )$$

A) Domain of $f : \left[ - \frac { 1 } { 9 } , \frac { 1 } { 9 } \right]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

B) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 5,5 ]$

C) Domain of f: $( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 9,9 ]$

D) Domain of f: $( \infty , \infty )$

Domain of $\mathrm { f } ^ { - 1 } : [ 4,14 ]$

Question 33

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $$f ( x ) = - 7 \cos ( 4 x )$$

A) $f ^ { - 1 } ( x ) = \frac { 1 } { 4 } \cos ^ { - 1 } \left( \frac { x } { 7 } \right)$
B) $f ^ { - 1 } ( x ) = - 7 \cos ^ { - 1 } ( 4 x )$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 7 } \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 4 } \right)$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 4 } \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 7 } \right)$

Question 34

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $f ( x ) = 3 \sin x - 2$

A) $f ^ { - 1 } ( x ) = 3 \sin ^ { - 1 } x - 2$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sin ^ { - 1 } \left( \frac { \mathrm { x } + 2 } { 3 } \right)$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \cos \left( \frac { \mathrm { x } + 2 } { 3 } \right)$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sin ^ { - 1 } \left( \frac { \mathrm { x } + 3 } { 2 } \right)$

Question 35

Find the exact value of the expression. Do not use a calculator.

- $$\sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 5 } \right) \right]$$

A) $5 \pi$
B) $\frac { \pi } { 5 }$
C) $- 5 \pi$
D) $- \frac { \pi } { 5 }$

Question 36

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = \cos ( x - 3 ) + 4$$

A) Domain of $f : ( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 5 , - 3 ]$

B) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 3,5 ]$

D) Domain of $f : [ - 3,3 ]$

Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

Question 37

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = - 8 \cos ( 10 x + 4 )$$

A) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

B) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 8,8 ]$

C) Domain of $\mathrm { f } : [ - 8,8 ]$
Domain of $f ^ { - 1 } : ( \infty , \infty )$

D) Domain of $\mathrm { f: } ( \infty , \infty )$

Domain of $f ^ { - 1 } : [ - 10,10 ]$

Question 38

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .

- $$f ( x ) = 3 \sin x - 5$$

A) Domain of $f$ : $[ 2,8 ]$
Domain of $\mathrm { f } ^ { - 1 } : [ - 8 , - 2 ]$

B) Domain of f: $( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 8 , - 2 ]$

C) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 2,8 ]$

D) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

Question 39

Find the inverse function $\mathrm { f } ^ { - 1 }$ of the function f.

- $$f ( x ) = - \sin ( x + 6 ) - 5$$

A) $f ^ { - 1 } ( x ) = - \sin ^ { - 1 } ( x - 5 ) + 6$
B) $f ^ { - 1 } ( x ) = - \sin ^ { - 1 } ( x + 6 ) - 5$
C) $f ^ { - 1 } ( x ) = - \sin ^ { - 1 } ( x + 5 ) - 6$
D) $f ^ { - 1 } ( x ) = \sin ^ { - 1 } ( x + 5 ) - 6$

Question 40

Find the exact solution of the equation.

- $\cos ^ { - 1 } x = 0$

A) x = -1
B) $x = \pi$
C) x = 1
D) x = 0

Question 41

Find the exact solution of the equation.

- $2 \cos ^ { - 1 } x = \pi$

A) $x = 0$
B) $x = 1$
C) $x = \frac { 3 \pi } { 2 }$
D) $x = \frac { \pi } { 2 }$

Question 42

Find the exact value of the expression.

- $$\sin ^ { - 1 } \left[ \sin \left( \frac { 6 \pi } { 7 } \right) \right]$$

A) $\frac { 6 \pi } { 7 }$
B) $\frac { 7 } { \pi }$
C) $\frac { \pi } { 7 }$
D) $\frac { 7 } { 6 \pi }$

Question 43

Find the exact solution of the equation.

- $$- \sin ^ { - 1 } ( 4 x ) = \frac { \pi } { 4 }$$

A) $x = - \frac { \sqrt { 2 } } { 8 }$
B) $x = \frac { \sqrt { 2 } } { 8 }$
C) $x = - \frac { \sqrt { 2 } } { 2 }$
D) $x = 0$

Question 44

Solve the problem.

Question 45

Solve the problem.
a

Question 46

Solve the problem.

Question 47

Find the exact value of the expression.

- $\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)$

A) $- \frac { 3 } { 5 }$
B) $\frac { 1 } { 5 }$
C) $- \frac { 4 } { 5 }$
D) $\frac { 3 } { 5 }$

Question 48

Find the exact value of the expression.

- $\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)$

A) $\frac { 2 \pi } { 3 }$
B) $\frac { 4 \pi } { 5 }$
C) $\frac { \pi } { 6 }$
D) $\frac { \pi } { 3 }$

Question 49

Find the exact value of the expression.

- $\cos ^ { - 1 } \left( \cos \frac { 7 \pi } { 6 } \right)$

A) $\frac { 4 \pi } { 5 }$
B) $\frac { \pi } { 6 }$
C) $\frac { \pi } { 3 }$
D) $\frac { 5 \pi } { 6 }$

Question 50

Find the exact value of the expression.

- $\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

A) $2 \sqrt { 2 }$
B) $2 \sqrt { 3 }$
C) $\frac { 2 \sqrt { 2 } } { 3 }$
D) $- 2 \sqrt { 3 }$

Question 51

Find the exact value of the expression.

- $$\cos ^ { - 1 } [ \cos ( - 0.9372 ) ]$$

A) -0.9372
B) 0.4686
C) -0.4686
D) 0.9372

Question 52

Find the exact solution of the equation.

- $$\sin ^ { - 1 } x = \frac { \pi } { 2 }$$

A) $x = 1$
B) $x = \pi$
C) $x = - 1$
D) $x = 0$

Question 53

Find the exact value of the expression.

- $\sin \left( \tan ^ { - 1 } 2 \right)$

A) $\frac { 5 \sqrt { 2 } } { 2 }$
B) $\frac { 2 \sqrt { 5 } } { 5 }$
C) $2 \sqrt { 5 }$
D) $5 \sqrt { 2 }$

Question 54

Solve the problem.
orth

Question 55

Find the exact solution of the equation.

- $$- 4 \tan ^ { - 1 } x = \pi$$

A) $x = 0$
B) $x = \frac { \pi } { 4 }$
C) $x = - 1$
D) $x = 1$

Question 56

Find the exact value of the expression.

- $\cos \left( \sin ^ { - 1 } \frac { 1 } { 4 } \right)$

A) $\frac { 2 \sqrt { 15 } } { 15 }$
B) $\frac { 4 \sqrt { 15 } } { 15 }$
C) $\frac { \sqrt { 15 } } { 4 }$
D) $\frac { \sqrt { 15 } } { 2 }$

Question 57

Find the exact solution of the equation.

- $$\sin ^ { - 1 } x = \frac { \pi } { 6 }$$

A) $x = - \frac { 1 } { 2 }$
B) $x = \frac { 1 } { 2 }$
C) $x = 0$
D) $x = 1$

Question 58

Find the exact value of the expression.

- $\cos \left[ \tan ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right) \right]$

A) $\frac { \pi } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { \sqrt { 3 } } { 3 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question 59

Solve the problem.

Question 60

Find the exact value of the expression.

- $\cos \left( 2 \sin ^ { - 1 } \frac { 1 } { 4 } \right)$

A) $\frac { 3 } { 8 }$
B) $\frac { 5 } { 8 }$
C) $\frac { 1 } { 8 }$
D) $\frac { 7 } { 8 }$

Question 61

Find the exact value of the composition.

- $\sin \left( \tan ^ { - 1 } ( 2 ) \right)$

A) $2 \sqrt { 5 }$
B) $\frac { 2 \sqrt { 5 } } { 5 }$
C) $\frac { 5 \sqrt { 2 } } { 2 }$
D) $5 \sqrt { 2 }$

Question 62

Find the exact value of the composition.

- $\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)$

A) $- \frac { 3 } { 5 }$
B) $\frac { 1 } { 5 }$
C) $- \frac { 4 } { 5 }$
D) $\frac { 3 } { 5 }$

Question 63

Find the exact value of the composition.

- $\sin \left( \tan ^ { - 1 } 2 \right)$

A) $\frac { 2 \sqrt { 5 } } { 5 }$
B) $2 \sqrt { 5 }$
C) $5 \sqrt { 2 }$
D) $\frac { 5 \sqrt { 2 } } { 2 }$

Question 64

Use a calculator to find the value of the expression in radian measure rounded to two decimal places.

- $\cot ^ { - 1 } \left( - \frac { 5 } { 7 } \right)$

A) -35.54
B) -0.95
C) -54.46
D) -0.62

Question 65

Find the exact value of the expression.

- $\sec ^ { - 1 } ( \sqrt { 2 } )$

A) $- \frac { 3 \pi } { 4 }$
B) $\frac { \pi } { 4 }$
C) $\frac { 3 \pi } { 4 }$
D) $\frac { \pi } { 3 }$

Question 66

Write the trigonometric expression as an algebraic expression in u.

- $\sin \left( \tan ^ { - 1 } u \right)$

A) $\frac { 1 } { \sqrt { u ^ { 2 } + 1 } }$
B) $\mathrm { u } \sqrt { \mathrm { u } ^ { 2 } + 1 }$
C) $\frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$
D) $\frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } - 1 } }$

Question 67

Find the exact value of the expression.

- $$\tan \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$$

A) 2
B) $\frac { \sqrt { 2 } } { 2 }$
C) $\sqrt { 2 }$
D) 1

Question 68

Find the exact value of the expression.

- $\cot ^ { - 1 } ( - 1 )$

A) $\frac { 2 \pi } { 3 }$
B) $\frac { 3 \pi } { 4 }$
C) $\frac { \pi } { 4 }$
D) $\frac { \pi } { 3 }$

Question 69

Use a calculator to find the value of the expression in radian measure rounded to two decimal places.

- $\sec ^ { - 1 } \left( - \frac { 7 } { 3 } \right)$

A) 2.01
B) -2.01
C) 0.50
D) 1.13

Question 70

Use a calculator to find the value of the expression in radian measure rounded to two decimal places.

- $\sec ^ { - 1 } \left( - \frac { 5 } { 4 } \right)$

A) 143.13
B) -0.93
C) 2.50
D) -53.13

Question 71

Find the exact value of the expression.

- $\tan ^ { - 1 } \left[ \tan \left( \frac { 6 \pi } { 7 } \right) \right]$

A) $- \frac { 6 \pi } { 7 }$
B) $\frac { \pi } { 7 }$
C) $\frac { 6 \pi } { 7 }$
D) $- \frac { \pi } { 7 }$

Question 72

Use a calculator to find the value of the expression in radian measure rounded to two decimal places.

- $$\csc ^ { - 1 } \left( - \frac { 7 } { 4 } \right)$$

A) $2.18$
B) $124.85$
C) $- 0.61$
D) $- 34.85$

Question 73

Find the exact value of the composition.

- $\cos \left( \sin ^ { - 1 } \left( \frac { 1 } { 4 } \right) \right)$

A) $\frac { \sqrt { 15 } } { 2 }$
B) $\frac { 2 \sqrt { 15 } } { 15 }$
C) $\frac { \sqrt { 15 } } { 4 }$
D) $\frac { 4 \sqrt { 15 } } { 15 }$

Question 74

Find the exact value of the expression.

- $$\sec \left[ \sin ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 2 } \right) \right]$$

A) 0
B) 2
C) $\frac { \sqrt { 2 } } { 2 }$
D) 1

Question 75

Find the exact value of the expression.

- $\csc ^ { - 1 } ( - 2 )$

A) $\frac { 2 \pi } { 3 }$
B) $\frac { \pi } { 3 }$
C) $- \frac { \pi } { 6 }$
D) $\frac { \pi } { 6 }$

Question 76

Find the exact value of the composition.

- $$\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)$$

A) $\frac { 2 \pi } { 3 }$
B) $\frac { 4 \pi } { 5 }$
C) $\frac { \pi } { 6 }$
D) $\frac { \pi } { 3 }$

Question 77

Write the trigonometric expression as an algebraic expression in u.

- $\cos \left( \tan ^ { - 1 } \mathrm { u } \right)$

A) $\mathrm { u } \sqrt { \mathrm { u } ^ { 2 } + 1 }$
B) $\frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$
C) $\frac { 1 } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$
D) $\frac { 1 } { \sqrt { u ^ { 2 } - 1 } }$

Question 78

Find the exact value of the expression.

- $\sec \left( \tan ^ { - 1 } \frac { \sqrt { 3 } } { 3 } \right)$

A) 2
B) $\frac { 2 \sqrt { 3 } } { 3 }$
C) $\frac { 1 } { 2 }$
D) $\sqrt { 3 }$

Question 79

Write the trigonometric expression as an algebraic expression in u.

- $\cos \left( \sin ^ { - 1 } u \right)$

A) $\sqrt { \mathrm { u } ^ { 2 } + 1 }$
B) $\sqrt { 1 - u ^ { 2 } }$
C) $\sqrt { \mathrm { u } ^ { 2 } - 1 }$
D) $\frac { \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } }$

Question 80

Find the exact value of the expression.

- $\sec ^ { - 1 } ( - 2 )$

A) $\frac { 2 \pi } { 3 }$
B) $- \frac { 2 \pi } { 3 }$
C) $- \frac { \pi } { 3 }$
D) $\frac { 4 \pi } { 3 }$