Question 1

Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$\cos \left( \sin ^ { - 1 } \mathrm { v } \right) =$ ?

Accepted Answer

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

Question 2

Write the word or phrase that best completes each statement or answers the question.
Use a calculator to solve the equation on the interval 0 . Round the answer to one decimal place if necessary. $$0 \leq x < 2 \pi$$
-$$e ^ { x } = \cos x$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
-$$\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Find the exact value of the composition.
-$$\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)$$

Accepted Answer

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

Question 5

Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$$\frac { \sin ( 2 \theta ) + 2 \sin ^ { 2 } \theta } { \cos ( 2 \theta ) } = ?$$

Accepted Answer

A)  $\frac { \tan ( 2 \theta ) + \tan ^ { 2 } \theta } { \sec ( 2 \theta ) }$ 
B)  $2 \tan \theta + 2$ 
C)  $\frac { 2 \tan \theta } { 1 - \tan \theta }$ 
D)  $\tan ( 2 \theta ) + 2 \tan ^ { 2 } \theta$ 
A)  $\frac { \tan ( 2 \theta ) + \tan ^ { 2 } \theta } { \sec ( 2 \theta ) }$ 
B)  $2 \tan \theta + 2$ 
C)  $\frac { 2 \tan \theta } { 1 - \tan \theta }$ 
D)  $\tan ( 2 \theta ) + 2 \tan ^ { 2 } \theta$

Question 6

Find the domain of the function f and of its inverse function f-1.
-$$f ( x ) = \tan ( x - 4 ) + 7$$

Accepted Answer

A)  Domain of $f : ( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 8 , - 6 ]$ 
B)  Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } + 7 ; k$ an integer 
Domain of $\mathrm { f } ^ { - 1 } : ( + , \infty )$ 
C)  Domain of $\mathrm { f } : \mathrm { x } \neq \frac { ( 2 \mathrm { k } + 1 ) \pi } { 2 } ; \mathrm { k }$ an integer
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$ 
D)  Domain of $\mathrm { f } : [ - 4,4 ]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$ 
A)  Domain of $f : ( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 8 , - 6 ]$ 
B)  Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } + 7 ; k$ an integer 
Domain of $\mathrm { f } ^ { - 1 } : ( + , \infty )$ 
C)  Domain of $\mathrm { f } : \mathrm { x } \neq \frac { ( 2 \mathrm { k } + 1 ) \pi } { 2 } ; \mathrm { k }$ an integer
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$ 
D)  Domain of $\mathrm { f } : [ - 4,4 ]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

Question 7

Find the exact value of the expression. Do not use a calculator.
-$\cos \left[ \cos ^ { - 1 } ( - 0.9372 ) \right]$

Accepted Answer

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

Question 8

Choose the one alternative that best completes the statement or answers the question.
Express the product as a sum containing only sines or cosines.
-$2 \cos ( 7 \theta ) \cos \theta$

Accepted Answer

A)  $\cos ( 10 \theta ) + \sin ( 4 \theta )$ 
B)  $\cos ( 14 \theta ) + \cos ( 2 \theta )$ 
C)  $\cos ( 8 \theta ) + \cos ( 6 \theta )$ 
D)  $\cos ( 8 \theta ) + \sin ( 6 \theta )$ 
A)  $\cos ( 10 \theta ) + \sin ( 4 \theta )$ 
B)  $\cos ( 14 \theta ) + \cos ( 2 \theta )$ 
C)  $\cos ( 8 \theta ) + \cos ( 6 \theta )$ 
D)  $\cos ( 8 \theta ) + \sin ( 6 \theta )$

Question 9

Use the Half-angle Formulas to find the exact value of the trigonometric function.
-$\cos 165 ^ { \circ }$

Accepted Answer

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

Question 10

Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$\ln | \cot x | =$ ?

Accepted Answer

A)  $\frac { \ln | \sin x | } { \ln | \cos x | }$ 
B)  $\frac { \ln | \cos x | } { \ln | \sin x | }$ 
C)  $\ln | \sin x | - \ln | \cos x |$ 
D)  $\ln | \cos x | - \ln | \sin x |$ 
A)  $\frac { \ln | \sin x | } { \ln | \cos x | }$ 
B)  $\frac { \ln | \cos x | } { \ln | \sin x | }$ 
C)  $\ln | \sin x | - \ln | \cos x |$ 
D)  $\ln | \cos x | - \ln | \sin x |$

Question 11

Express the sum or difference as a product of sines and/or cosines.
-$\cos ( 4 \theta ) - \cos ( 6 \theta )$

Accepted Answer

A)  $2 \sin ( 5 \theta ) \sin \theta$ 
B)  $\cos ( - 2 \theta )$ 
C)  $- 2 \cos ( 5 \theta ) \sin \theta$ 
D)  $- 2 \sin ( 5 \theta ) \sin \theta$ 
A)  $2 \sin ( 5 \theta ) \sin \theta$ 
B)  $\cos ( - 2 \theta )$ 
C)  $- 2 \cos ( 5 \theta ) \sin \theta$ 
D)  $- 2 \sin ( 5 \theta ) \sin \theta$

Question 12

Find the exact value of the expression.
-$\cos \left( \sin ^ { - 1 } \frac { 1 } { 3 } - \tan ^ { - 1 } \frac { 1 } { 2 } \right)$

Accepted Answer

A)  $\frac { 2 \sqrt { 3 } + 4 } { 3 \sqrt { 5 } }$ 
B)  $\frac { 2 \sqrt { 6 } } { 5 }$ 
C)  $\frac { 4 \sqrt { 10 } + \sqrt { 5 } } { 15 }$ 
D)  $\frac { 2 \sqrt { 3 } + 1 } { 5 }$ 
A)  $\frac { 2 \sqrt { 3 } + 4 } { 3 \sqrt { 5 } }$ 
B)  $\frac { 2 \sqrt { 6 } } { 5 }$ 
C)  $\frac { 4 \sqrt { 10 } + \sqrt { 5 } } { 15 }$ 
D)  $\frac { 2 \sqrt { 3 } + 1 } { 5 }$

Question 13

Express the sum or difference as a product of sines and/or cosines.
-$$\sin \frac { 7 \theta } { 2 } + \sin \frac { 3 \theta } { 2 }$$

Accepted Answer

A)  $2 \sin \frac { 5 \theta } { 2 } \sin \theta$ 
B)  $2 \sin ( 5 \theta )$ 
C)  $2 \cos ( 5 \theta ) \sin \theta$ 
D)  $2 \sin \frac { 5 \theta } { 2 } \cos \theta$ 
A)  $2 \sin \frac { 5 \theta } { 2 } \sin \theta$ 
B)  $2 \sin ( 5 \theta )$ 
C)  $2 \cos ( 5 \theta ) \sin \theta$ 
D)  $2 \sin \frac { 5 \theta } { 2 } \cos \theta$

Question 14

Write the word or phrase that best completes each statement or answers the question.
-$$- 11 + 24 \sin x = 16 \cos ^ { 2 } x$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Find the exact value under the given conditions.
-$\sin \alpha = \frac { 3 } { 5 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \cos \beta = \frac { 2 } { 5 } , 0 < \beta < \frac { \pi } { 2 }$
Find $\cos ( \alpha - \beta )$

Accepted Answer

A)  $\frac { 8 - 3 \sqrt { 21 } } { 25 }$ 
B)  $\frac { 6 + 4 \sqrt { 21 } } { 25 }$ 
C)  $\frac { 6 - 4 \sqrt { 21 } } { 25 }$ 
D)  $\frac { - 8 + 3 \sqrt { 21 } } { 25 }$ 
A)  $\frac { 8 - 3 \sqrt { 21 } } { 25 }$ 
B)  $\frac { 6 + 4 \sqrt { 21 } } { 25 }$ 
C)  $\frac { 6 - 4 \sqrt { 21 } } { 25 }$ 
D)  $\frac { - 8 + 3 \sqrt { 21 } } { 25 }$

Question 16

Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
-$$\frac { 5 \csc ^ { 2 } x + 4 \csc x - 1 } { \cot ^ { 2 } x } = \frac { 5 \csc x - 1 } { \csc x - 1 }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Find the exact value of the expression.
-$\sin 10 ^ { \circ } \cos 50 ^ { \circ } + \cos 10 ^ { \circ } \sin 50 ^ { \circ }$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { \sqrt { 3 } } { 3 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 6 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { \sqrt { 3 } } { 3 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 6 }$

Question 18

Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$$\frac { \sin \theta } { 1 + \sin \theta } - \frac { \sin \theta } { 1 - \sin \theta } = ?$$

Accepted Answer

A)  $\sin \theta \tan \theta$ 
B)  $1 + \cot \theta$ 
C)  $\sec \theta \csc \theta$ 
D)  $- 2 \tan ^ { 2 } \theta$ 
A)  $\sin \theta \tan \theta$ 
B)  $1 + \cot \theta$ 
C)  $\sec \theta \csc \theta$ 
D)  $- 2 \tan ^ { 2 } \theta$

Question 19

Use a calculator to find the value of the expression rounded to two decimal places.
-$\sin ^ { - 1 } ( 0.7 )$

Accepted Answer

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

Question 20

Simplify the trigonometric expression by following the indicated direction.
-$$\text { Rewrite in terms of sine and } \operatorname { cosine } : \tan x \cdot \cot x$$

Accepted Answer

The answer of Simplify the trigonometric expression by following the...

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\cos \left( \sin ^ { - 1 } \mathrm { v } \right) =$ ?

Write the word or phrase that best completes each statement or answers the question. Use a calculator to solve the equation on the interval 0 . Round the answer to one decimal place if necessary. $0 \leq x < 2 \pi$ - $e ^ { x } = \cos x$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )$

Find the exact value of the composition. - $\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\frac { \sin ( 2 \theta ) + 2 \sin ^ { 2 } \theta } { \cos ( 2 \theta ) } = ?$

Find the domain of the function f and of its inverse function f-1. - $f ( x ) = \tan ( x - 4 ) + 7$

Find the exact value of the expression. Do not use a calculator. - $\cos \left[ \cos ^ { - 1 } ( - 0.9372 ) \right]$

Choose the one alternative that best completes the statement or answers the question. Express the product as a sum containing only sines or cosines. - $2 \cos ( 7 \theta ) \cos \theta$

Use the Half-angle Formulas to find the exact value of the trigonometric function. - $\cos 165 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\ln | \cot x | =$ ?

Express the sum or difference as a product of sines and/or cosines. - $\cos ( 4 \theta ) - \cos ( 6 \theta )$

Find the exact value of the expression. - $\cos \left( \sin ^ { - 1 } \frac { 1 } { 3 } - \tan ^ { - 1 } \frac { 1 } { 2 } \right)$

Express the sum or difference as a product of sines and/or cosines. - $\sin \frac { 7 \theta } { 2 } + \sin \frac { 3 \theta } { 2 }$

Write the word or phrase that best completes each statement or answers the question. - $- 11 + 24 \sin x = 16 \cos ^ { 2 } x$

Find the exact value under the given conditions. - $\sin \alpha = \frac { 3 } { 5 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \cos \beta = \frac { 2 } { 5 } , 0 < \beta < \frac { \pi } { 2 }$ Find $\cos ( \alpha - \beta )$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\frac { 5 \csc ^ { 2 } x + 4 \csc x - 1 } { \cot ^ { 2 } x } = \frac { 5 \csc x - 1 } { \csc x - 1 }$

Find the exact value of the expression. - $\sin 10 ^ { \circ } \cos 50 ^ { \circ } + \cos 10 ^ { \circ } \sin 50 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\frac { \sin \theta } { 1 + \sin \theta } - \frac { \sin \theta } { 1 - \sin \theta } = ?$

Use a calculator to find the value of the expression rounded to two decimal places. - $\sin ^ { - 1 } ( 0.7 )$

Simplify the trigonometric expression by following the indicated direction. - $\text { Rewrite in terms of sine and } \operatorname { cosine } : \tan x \cdot \cot x$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 6: Analytic Trigonometry

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - cos⁡(sin⁡−1v)=\cos \left( \sin ^ { - 1 } \mathrm { v } \right) =cos(sin−1v)= ?

Write the word or phrase that best completes each statement or answers the question. Use a calculator to solve the equation on the interval 0 . Round the answer to one decimal place if necessary. 0≤x<2π0 \leq x < 2 \pi0≤x<2π - ex=cos⁡xe ^ { x } = \cos xex=cosx

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - cot⁡2x=(csc⁡x−1)(csc⁡x+1)\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )cot2x=(cscx−1)(cscx+1)

Find the exact value of the composition. - cos⁡−1(sin⁡7π6)\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)cos−1(sin67π​)

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - sin⁡(2θ)+2sin⁡2θcos⁡(2θ)=?\frac { \sin ( 2 \theta ) + 2 \sin ^ { 2 } \theta } { \cos ( 2 \theta ) } = ?cos(2θ)sin(2θ)+2sin2θ​=?

Find the domain of the function f and of its inverse function f-1. - f(x)=tan⁡(x−4)+7f ( x ) = \tan ( x - 4 ) + 7f(x)=tan(x−4)+7

Find the exact value of the expression. Do not use a calculator. - cos⁡[cos⁡−1(−0.9372)]\cos \left[ \cos ^ { - 1 } ( - 0.9372 ) \right]cos[cos−1(−0.9372)]

Choose the one alternative that best completes the statement or answers the question. Express the product as a sum containing only sines or cosines. - 2cos⁡(7θ)cos⁡θ2 \cos ( 7 \theta ) \cos \theta2cos(7θ)cosθ

Use the Half-angle Formulas to find the exact value of the trigonometric function. - cos⁡165∘\cos 165 ^ { \circ }cos165∘

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - ln⁡∣cot⁡x∣=\ln | \cot x | =ln∣cotx∣= ?

Express the sum or difference as a product of sines and/or cosines. - cos⁡(4θ)−cos⁡(6θ)\cos ( 4 \theta ) - \cos ( 6 \theta )cos(4θ)−cos(6θ)

Find the exact value of the expression. - cos⁡(sin⁡−113−tan⁡−112)\cos \left( \sin ^ { - 1 } \frac { 1 } { 3 } - \tan ^ { - 1 } \frac { 1 } { 2 } \right)cos(sin−131​−tan−121​)

Express the sum or difference as a product of sines and/or cosines. - sin⁡7θ2+sin⁡3θ2\sin \frac { 7 \theta } { 2 } + \sin \frac { 3 \theta } { 2 }sin27θ​+sin23θ​

Write the word or phrase that best completes each statement or answers the question. - −11+24sin⁡x=16cos⁡2x- 11 + 24 \sin x = 16 \cos ^ { 2 } x−11+24sinx=16cos2x

Find the exact value of the expression. - sin⁡10∘cos⁡50∘+cos⁡10∘sin⁡50∘\sin 10 ^ { \circ } \cos 50 ^ { \circ } + \cos 10 ^ { \circ } \sin 50 ^ { \circ }sin10∘cos50∘+cos10∘sin50∘

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - sin⁡θ1+sin⁡θ−sin⁡θ1−sin⁡θ=?\frac { \sin \theta } { 1 + \sin \theta } - \frac { \sin \theta } { 1 - \sin \theta } = ?1+sinθsinθ​−1−sinθsinθ​=?

Use a calculator to find the value of the expression rounded to two decimal places. - sin⁡−1(0.7)\sin ^ { - 1 } ( 0.7 )sin−1(0.7)

Simplify the trigonometric expression by following the indicated direction. - Rewrite in terms of sine and cosine⁡:tan⁡x⋅cot⁡x\text { Rewrite in terms of sine and } \operatorname { cosine } : \tan x \cdot \cot x Rewrite in terms of sine and cosine:tanx⋅cotx

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\cos \left( \sin ^ { - 1 } \mathrm { v } \right) =$ ?

Write the word or phrase that best completes each statement or answers the question. Use a calculator to solve the equation on the interval 0 . Round the answer to one decimal place if necessary. $0 \leq x < 2 \pi$ - $e ^ { x } = \cos x$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )$

Find the exact value of the composition. - $\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\frac { \sin ( 2 \theta ) + 2 \sin ^ { 2 } \theta } { \cos ( 2 \theta ) } = ?$

Find the domain of the function f and of its inverse function f-1. - $f ( x ) = \tan ( x - 4 ) + 7$

Find the exact value of the expression. Do not use a calculator. - $\cos \left[ \cos ^ { - 1 } ( - 0.9372 ) \right]$

Choose the one alternative that best completes the statement or answers the question. Express the product as a sum containing only sines or cosines. - $2 \cos ( 7 \theta ) \cos \theta$

Use the Half-angle Formulas to find the exact value of the trigonometric function. - $\cos 165 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\ln | \cot x | =$ ?

Express the sum or difference as a product of sines and/or cosines. - $\cos ( 4 \theta ) - \cos ( 6 \theta )$

Find the exact value of the expression. - $\cos \left( \sin ^ { - 1 } \frac { 1 } { 3 } - \tan ^ { - 1 } \frac { 1 } { 2 } \right)$

Express the sum or difference as a product of sines and/or cosines. - $\sin \frac { 7 \theta } { 2 } + \sin \frac { 3 \theta } { 2 }$

Write the word or phrase that best completes each statement or answers the question. - $- 11 + 24 \sin x = 16 \cos ^ { 2 } x$

Find the exact value of the expression. - $\sin 10 ^ { \circ } \cos 50 ^ { \circ } + \cos 10 ^ { \circ } \sin 50 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\frac { \sin \theta } { 1 + \sin \theta } - \frac { \sin \theta } { 1 - \sin \theta } = ?$

Use a calculator to find the value of the expression rounded to two decimal places. - $\sin ^ { - 1 } ( 0.7 )$

Simplify the trigonometric expression by following the indicated direction. - $\text { Rewrite in terms of sine and } \operatorname { cosine } : \tan x \cdot \cot x$