Question 1

Find the exact solution of the equation.
-$- 4 \tan ^ { - 1 } x = \pi$

Accepted Answer

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

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find $\sin \theta$, given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $0 < \theta < \frac { \pi } { 2 }$.

Accepted Answer

A)  $\frac { \sqrt { 8 - 2 \sqrt { 10 } } } { 4 }$ 
B)  $\frac { \sqrt { 10 - 2 \sqrt { 6 } } } { 4 }$ 
C)  $\frac { \sqrt { 6 } } { 4 }$ 
D)  $\frac { \sqrt { 10 } } { 4 }$ 
A)  $\frac { \sqrt { 8 - 2 \sqrt { 10 } } } { 4 }$ 
B)  $\frac { \sqrt { 10 - 2 \sqrt { 6 } } } { 4 }$ 
C)  $\frac { \sqrt { 6 } } { 4 }$ 
D)  $\frac { \sqrt { 10 } } { 4 }$

Question 3

Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$( 4 \sin \theta \cos \theta ) \left( 1 - 2 \sin ^ { 2 } \theta \right) =$ ?

Accepted Answer

A)  $\sin ( 4 \theta )$ 
B)  $\sin ( 2 \theta ) + \cos ( 2 \theta )$ 
C)  $\frac { \cos ( 4 \theta ) } { \sin ( 2 \theta ) }$ 
D)  $\sin ( 2 \theta ) \cos ( 2 \theta )$ 
A)  $\sin ( 4 \theta )$ 
B)  $\sin ( 2 \theta ) + \cos ( 2 \theta )$ 
C)  $\frac { \cos ( 4 \theta ) } { \sin ( 2 \theta ) }$ 
D)  $\sin ( 2 \theta ) \cos ( 2 \theta )$

Question 4

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

Accepted Answer

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

Question 5

Choose the one alternative that best completes the statement or answers the question.
-$\sin ^ { 2 } x - 8 \sin x - 4 = 0$

Accepted Answer

A)  $28.2 ^ { \circ } , 151.8 ^ { \circ } , 208.2 ^ { \circ } , 331.8 ^ { \circ }$ 
B)  $28.2 ^ { \circ } , 151.8 ^ { \circ }$ 
C)  $208.2 ^ { \circ } , 331.8 ^ { \circ }$ 
D)  No solution 
A)  $28.2 ^ { \circ } , 151.8 ^ { \circ } , 208.2 ^ { \circ } , 331.8 ^ { \circ }$ 
B)  $28.2 ^ { \circ } , 151.8 ^ { \circ }$ 
C)  $208.2 ^ { \circ } , 331.8 ^ { \circ }$ 
D)  No solution

Question 6

Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
-$$\sin \left( x - \frac { \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } ( \sin x - \cos x )$$

Accepted Answer

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

Question 7

Find the exact value of the expression. Do not use a calculator.
-$\cos ^ { - 1 } \left[ \cos \left( - \frac { 3 \pi } { 5 } \right) \right]$

Accepted Answer

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

Question 8

Find the exact value under the given conditions.
-$\cos \alpha = - \frac { 4 } { 5 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = - \frac { \sqrt { 21 } } { 5 } , \pi < \beta < \frac { 3 \pi } { 2 } \quad$ Find $\cos ( \alpha + \beta )$.

Accepted Answer

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

Question 9

Use a calculator to find the value of the expression in radian measure rounded to two decimal places.
-$\cot ^ { - 1 } \left( - \frac { 5 } { 7 } \right)$

Accepted Answer

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

Question 10

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-A weight is suspended on a system of spring and oscillates up and down according to $$P = 0.1 [ 3 \cos ( 8 t ) - \sin ( 8 t ) ]$$
where $P$ is the position in meters above or below the point of equilibrium $( P = 0 )$ and $t$ is time in seconds. Find th time when the weight is at equilibrium. Find all values of $t , 0 \leq t \leq 1$, rounded to the nearest $0.01$ second.

Accepted Answer

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

Question 11

Find the exact value of the expression.
-$\cos \left( \frac { 7 \pi } { 12 } \right) \cos \left( \frac { 5 \pi } { 12 } \right) + \sin \left( \frac { 7 \pi } { 12 } \right) \sin \left( \frac { 5 \pi } { 12 } \right)$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  1 
D)  $\frac { \sqrt { 3 } } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  1 
D)  $\frac { \sqrt { 3 } } { 2 }$

Question 12

Solve the equation. Give a general formula for all the solutions.
-$\sin \theta = 0$

Accepted Answer

A)  $\theta = \frac { \pi } { 2 } + \mathrm { k } \pi$ 
B)  $\theta = \frac { \pi } { 2 } + 2 \mathrm { k } \pi$ 
C)  $\theta = 0 + \mathrm { k } \pi$ 
D)  $\theta = 0 + 2 \mathrm { k } \pi$ 
A)  $\theta = \frac { \pi } { 2 } + \mathrm { k } \pi$ 
B)  $\theta = \frac { \pi } { 2 } + 2 \mathrm { k } \pi$ 
C)  $\theta = 0 + \mathrm { k } \pi$ 
D)  $\theta = 0 + 2 \mathrm { k } \pi$

Question 13

Find the exact value under the given conditions.
-$\cos \alpha = \frac { 1 } { 3 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \sin \beta = - \frac { 1 } { 2 } , - \frac { \pi } { 2 } < \beta < 0 \quad$ Find $\tan ( \alpha + \beta )$.

Accepted Answer

A)  $\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 3 }$ 
B)  $\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 5 }$ 
C)  $\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 5 }$ 
D)  $\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 3 }$ 
A)  $\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 3 }$ 
B)  $\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 5 }$ 
C)  $\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 5 }$ 
D)  $\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 3 }$

Question 14

Find the exact value of the expression.
-$$\sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 }$$

Accepted Answer

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

Question 15

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

Accepted Answer

A)  $\cos ^ { 3 } \theta$ 
B)  $\tan ^ { 2 } \theta$ 
C)  $\sin \theta$ 
D)  $\sec ^ { 2 } \theta$ 
A)  $\cos ^ { 3 } \theta$ 
B)  $\tan ^ { 2 } \theta$ 
C)  $\sin \theta$ 
D)  $\sec ^ { 2 } \theta$

Question 16

Find the exact value of the expression.
-$$\cos ^ { - 1 } \frac { \sqrt { 3 } } { 2 }$$

Accepted Answer

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

Question 17

Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression.
-$\cos \left( \sin ^ { - 1 } \frac { 1 } { 4 } \right)$

Accepted Answer

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

Question 18

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

Accepted Answer

A)  $\frac { 2 } { 1 - \cos \theta }$ 
B)  $\frac { 1 - \sec \theta } { 2 }$ 
C)  $\frac { 2 } { 1 + \sin \theta }$ 
D)  $\frac { 1 + \sec \theta } { 2 }$ 
A)  $\frac { 2 } { 1 - \cos \theta }$ 
B)  $\frac { 1 - \sec \theta } { 2 }$ 
C)  $\frac { 2 } { 1 + \sin \theta }$ 
D)  $\frac { 1 + \sec \theta } { 2 }$

Question 19

Find the domain of the function f and of its inverse function f-1.
-$$f ( x ) = - 5 \cos ( 9 x )$$

Accepted Answer

A)  Domain of $f : \left[ - \frac { 1 } { 9 } , \frac { 1 } { 9 } \right]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$ 
B)  Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 5,5 ]$ 
C)  Domain of f: $( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 9,9 ]$ 
D)  Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 4,14 ]$ 
A)  Domain of $f : \left[ - \frac { 1 } { 9 } , \frac { 1 } { 9 } \right]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$ 
B)  Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 5,5 ]$ 
C)  Domain of f: $( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 9,9 ]$ 
D)  Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 4,14 ]$

Question 20

Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
-$$\tan \left( \frac { \pi } { 2 } + x \right) = - \cot x$$

Accepted Answer

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

Find the exact solution of the equation. - $- 4 \tan ^ { - 1 } x = \pi$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find $\sin \theta$ , given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $0 < \theta < \frac { \pi } { 2 }$ .

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $( 4 \sin \theta \cos \theta ) \left( 1 - 2 \sin ^ { 2 } \theta \right) =$ ?

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

Choose the one alternative that best completes the statement or answers the question. - $\sin ^ { 2 } x - 8 \sin x - 4 = 0$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\sin \left( x - \frac { \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } ( \sin x - \cos x )$

Find the exact value of the expression. Do not use a calculator. - $\cos ^ { - 1 } \left[ \cos \left( - \frac { 3 \pi } { 5 } \right) \right]$

Find the exact value under the given conditions. - $\cos \alpha = - \frac { 4 } { 5 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = - \frac { \sqrt { 21 } } { 5 } , \pi < \beta < \frac { 3 \pi } { 2 } \quad$ Find $\cos ( \alpha + \beta )$ .

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. - $\cot ^ { - 1 } \left( - \frac { 5 } { 7 } \right)$

Find the exact value of the expression. - $\cos \left( \frac { 7 \pi } { 12 } \right) \cos \left( \frac { 5 \pi } { 12 } \right) + \sin \left( \frac { 7 \pi } { 12 } \right) \sin \left( \frac { 5 \pi } { 12 } \right)$

Solve the equation. Give a general formula for all the solutions. - $\sin \theta = 0$

Find the exact value under the given conditions. - $\cos \alpha = \frac { 1 } { 3 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \sin \beta = - \frac { 1 } { 2 } , - \frac { \pi } { 2 } < \beta < 0 \quad$ Find $\tan ( \alpha + \beta )$ .

Find the exact value of the expression. - $\sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 }$

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

Find the exact value of the expression. - $\cos ^ { - 1 } \frac { \sqrt { 3 } } { 2 }$

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\cos \left( \sin ^ { - 1 } \frac { 1 } { 4 } \right)$

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

Find the domain of the function f and of its inverse function f-1. - $f ( x ) = - 5 \cos ( 9 x )$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\tan \left( \frac { \pi } { 2 } + x \right) = - \cot x$

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

Find the exact solution of the equation. - −4tan⁡−1x=π- 4 \tan ^ { - 1 } x = \pi−4tan−1x=π

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find sin⁡θ\sin \thetasinθ , given that cos⁡2θ=14\cos 2 \theta = \frac { 1 } { 4 }cos2θ=41​ and 0<θ<π20 < \theta < \frac { \pi } { 2 }0<θ<2π​ .

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - (4sin⁡θcos⁡θ)(1−2sin⁡2θ)=( 4 \sin \theta \cos \theta ) \left( 1 - 2 \sin ^ { 2 } \theta \right) =(4sinθcosθ)(1−2sin2θ)= ?

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

Choose the one alternative that best completes the statement or answers the question. - sin⁡2x−8sin⁡x−4=0\sin ^ { 2 } x - 8 \sin x - 4 = 0sin2x−8sinx−4=0

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - sin⁡(x−π4)=22(sin⁡x−cos⁡x)\sin \left( x - \frac { \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } ( \sin x - \cos x )sin(x−4π​)=22​​(sinx−cosx)

Find the exact value of the expression. Do not use a calculator. - cos⁡−1[cos⁡(−3π5)]\cos ^ { - 1 } \left[ \cos \left( - \frac { 3 \pi } { 5 } \right) \right]cos−1[cos(−53π​)]

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. - cot⁡−1(−57)\cot ^ { - 1 } \left( - \frac { 5 } { 7 } \right)cot−1(−75​)

Solve the equation. Give a general formula for all the solutions. - sin⁡θ=0\sin \theta = 0sinθ=0

Find the exact value of the expression. - sin⁡−122\sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 }sin−122​​

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - cos⁡θ−cos⁡θsin⁡2θ=\cos \theta - \cos \theta \sin ^ { 2 } \theta =cosθ−cosθsin2θ= ?

Find the exact value of the expression. - cos⁡−132\cos ^ { - 1 } \frac { \sqrt { 3 } } { 2 }cos−123​​

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - cos⁡(sin⁡−114)\cos \left( \sin ^ { - 1 } \frac { 1 } { 4 } \right)cos(sin−141​)

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - csc⁡2θ2=?\csc ^ { 2 } \frac { \theta } { 2 } = ?csc22θ​=?

Find the domain of the function f and of its inverse function f-1. - f(x)=−5cos⁡(9x)f ( x ) = - 5 \cos ( 9 x )f(x)=−5cos(9x)

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - tan⁡(π2+x)=−cot⁡x\tan \left( \frac { \pi } { 2 } + x \right) = - \cot xtan(2π​+x)=−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

Find the exact solution of the equation. - $- 4 \tan ^ { - 1 } x = \pi$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find $\sin \theta$ , given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $0 < \theta < \frac { \pi } { 2 }$ .

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $( 4 \sin \theta \cos \theta ) \left( 1 - 2 \sin ^ { 2 } \theta \right) =$ ?

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

Choose the one alternative that best completes the statement or answers the question. - $\sin ^ { 2 } x - 8 \sin x - 4 = 0$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\sin \left( x - \frac { \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } ( \sin x - \cos x )$

Find the exact value of the expression. Do not use a calculator. - $\cos ^ { - 1 } \left[ \cos \left( - \frac { 3 \pi } { 5 } \right) \right]$

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. - $\cot ^ { - 1 } \left( - \frac { 5 } { 7 } \right)$

Solve the equation. Give a general formula for all the solutions. - $\sin \theta = 0$

Find the exact value of the expression. - $\sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 }$

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

Find the exact value of the expression. - $\cos ^ { - 1 } \frac { \sqrt { 3 } } { 2 }$

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\cos \left( \sin ^ { - 1 } \frac { 1 } { 4 } \right)$

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

Find the domain of the function f and of its inverse function f-1. - $f ( x ) = - 5 \cos ( 9 x )$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\tan \left( \frac { \pi } { 2 } + x \right) = - \cot x$