Question 1

Find the inverse function f-1 of the function f.
-$$f ( x ) = - \sin ( x + 6 ) - 5$$

Accepted Answer

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)  $f ^ { - 1 } ( x ) = \sin ^ { - 1 } ( x + 5 ) - 6$ 
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 2

Write the word or phrase that best completes each statement or answers the question.
-A mass hangs from a spring which oscillates up and down. The position $\mathrm { P }$ (in feet) of the mass at time $t$ (in secon given by
$$P = 4 \cos ( 4 \mathrm { t } )$$
For what values of $t , 0 \leq t < \pi$, will the position be $2 \sqrt { 2 }$ feet? Find the exact values. Do not use a calculator.

Accepted Answer

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

Question 3

Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$\sec ^ { 4 } \theta + \sec ^ { 2 } \theta \tan ^ { 2 } \theta - 2 \tan ^ { 4 } \theta =$ ?

Accepted Answer

A)  $4 \sec ^ { 2 } \theta$ 
B)  $\sec ^ { 2 } \theta + 2$ 
C)  $\tan ^ { 2 } \theta - 1$ 
D)  $3 \sec ^ { 2 } \theta - 2$ 
A)  $4 \sec ^ { 2 } \theta$ 
B)  $\sec ^ { 2 } \theta + 2$ 
C)  $\tan ^ { 2 } \theta - 1$ 
D)  $3 \sec ^ { 2 } \theta - 2$

Question 4

Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
-$$\cos \left( x + \frac { \pi } { 6 } \right) = \frac { \sqrt { 3 } } { 2 } \cos x - \frac { 1 } { 2 } \sin x$$

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression.
-$$\tan \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$$

Accepted Answer

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

Question 7

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The formula
$$\mathrm { D } = 24 \left[ 1 - \frac { \cos ^ { - 1 } ( \tan \mathrm { i } \tan \theta ) } { \pi } \right]$$ can be used to approximate the number of hours of daylight when the declination of the sun is i orth $$i ^ { \circ } \text { at a location } \theta ^ { \circ }$$ latitude for any date between the vernal equinox and autumnal equinox. To use this formula, $$\cos ^ { - 1 } ( \tan i \tan \theta )$$ must be expressed in radians. Approximate the number of hours of daylight in Fargo, North Dakota,
for vernal equinox $\text { ( } 46 ^ { \circ } 52 ^ { \prime } \text { north latitude) }$ $\left( \mathrm { i } = 0 ^ { \circ } \right)$

Accepted Answer

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

Question 8

Find the exact value under the given conditions.
-$\cos \alpha = - \frac { 5 } { 13 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = \frac { 8 } { 17 } , \frac { \pi } { 2 } < \alpha < \pi \quad$ Find $\tan ( \alpha - \beta ) .$

Accepted Answer

A)  $\frac { 50 } { 19 }$ 
B)  $\frac { 20 } { 3 }$ 
C)  $- \frac { 20 } { 3 }$ 
D)  $- \frac { 140 } { 171 }$ 
A)  $\frac { 50 } { 19 }$ 
B)  $\frac { 20 } { 3 }$ 
C)  $- \frac { 20 } { 3 }$ 
D)  $- \frac { 140 } { 171 }$

Question 9

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

Accepted Answer

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

Question 10

Write the trigonometric expression as an algebraic expression in u.
-$\sin \left( \tan ^ { - 1 } u \right)$

Accepted Answer

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

Question 11

Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression.
-$\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

Accepted Answer

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

Question 12

Find the exact value under the given conditions.
-$\sin \alpha = \frac { 20 } { 29 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \cos \beta = \frac { 3 } { 5 } , 0 < \beta < \frac { \pi } { 2 } \quad$ Find $\sin ( \alpha - \beta )$.

Accepted Answer

A)  $\frac { 143 } { 145 }$ 
B)  $- \frac { 17 } { 145 }$ 
C)  $\frac { 144 } { 145 }$ 
D)  $- \frac { 24 } { 145 }$ 
A)  $\frac { 143 } { 145 }$ 
B)  $- \frac { 17 } { 145 }$ 
C)  $\frac { 144 } { 145 }$ 
D)  $- \frac { 24 } { 145 }$

Question 13

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

Accepted Answer

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

Question 14

Choose the one alternative that best completes the statement or answers the question.
-$\cos ^ { 2 } x + \cos x - 1 = 0$

Accepted Answer

A)  $103.2 ^ { \circ } , 145.2 ^ { \circ } , 283.2 ^ { \circ } , 325.2 ^ { \circ }$ 
B)  $49.8 ^ { \circ } , 130.2 ^ { \circ } , 229.8 ^ { \circ } , 310.2 ^ { \circ }$ 
C)  $51.8 ^ { \circ } , 308.2 ^ { \circ }$ 
D)  $70.5 ^ { \circ } , 109.5 ^ { \circ } , 180.0 ^ { \circ }$ 
A)  $103.2 ^ { \circ } , 145.2 ^ { \circ } , 283.2 ^ { \circ } , 325.2 ^ { \circ }$ 
B)  $49.8 ^ { \circ } , 130.2 ^ { \circ } , 229.8 ^ { \circ } , 310.2 ^ { \circ }$ 
C)  $51.8 ^ { \circ } , 308.2 ^ { \circ }$ 
D)  $70.5 ^ { \circ } , 109.5 ^ { \circ } , 180.0 ^ { \circ }$

Question 15

Write the word or phrase that best completes each statement or answers the question.
-You are flying a kite and want to know its angle of elevation. The string on the kite is 43 meters long and the
kite is level with the top of a building that you know is 28 meters high. Use an inverse trigonometric function to
find the angle of elevation of the kite. Round to two decimal places.

Accepted Answer

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

Question 16

Solve the problem.
-If $\tan \theta = \frac { 7 } { 24 }$, and $\theta$ terminates in quadrant III, then find $\cos 2 \theta$.

Accepted Answer

A)  $\frac { 527 } { 625 }$ 
B)  $- \frac { 527 } { 625 }$ 
C)  $\frac { 336 } { 625 }$ 
D)  $- \frac { 336 } { 625 }$ 
A)  $\frac { 527 } { 625 }$ 
B)  $- \frac { 527 } { 625 }$ 
C)  $\frac { 336 } { 625 }$ 
D)  $- \frac { 336 } { 625 }$

Question 17

Choose the one alternative that best completes the statement or answers the question.
Express the product as a sum containing only sines or cosines.
-$\cos ( 5 \theta ) \cos ( 4 \theta )$

Accepted Answer

A)  $\frac { 1 } { 2 } [ \cos ( 9 \theta ) - \cos \theta ]$ 
B)  $\frac { 1 } { 2 } [ \cos \theta + \cos ( 9 \theta ) ]$ 
C)  $\cos ^ { 2 } \left( 20 \theta ^ { 2 } \right)$ 
D)  $\frac { 1 } { 2 } [ \cos ( 9 \theta ) - \sin \theta ]$ 
A)  $\frac { 1 } { 2 } [ \cos ( 9 \theta ) - \cos \theta ]$ 
B)  $\frac { 1 } { 2 } [ \cos \theta + \cos ( 9 \theta ) ]$ 
C)  $\cos ^ { 2 } \left( 20 \theta ^ { 2 } \right)$ 
D)  $\frac { 1 } { 2 } [ \cos ( 9 \theta ) - \sin \theta ]$

Question 18

Simplify the expression.
-$4 \sin \theta \cos ^ { 3 } \theta - 4 \sin ^ { 3 } \theta \cos \theta$

Accepted Answer

A)  $\sin 4 \theta$ 
B)  $4 \sin \theta \cos \theta \cos 2 \theta$ 
C)  $\sin 2 \theta \cos 2 \theta$ 
D)  $4 \sin \theta \cos \theta$ 
A)  $\sin 4 \theta$ 
B)  $4 \sin \theta \cos \theta \cos 2 \theta$ 
C)  $\sin 2 \theta \cos 2 \theta$ 
D)  $4 \sin \theta \cos \theta$

Question 19

Express the sum or difference as a product of sines and/or cosines.
-$\cos ( 10 \theta ) - \cos ( 4 \theta )$

Accepted Answer

A)  $2 \cos ( 3 \theta )$ 
B)  $2 \cos ( 7 \theta ) \cos ( 3 \theta )$ 
C)  $- 2 \sin ( 7 \theta ) \sin ( 3 \theta )$ 
D)  $- 2 \cos ( 7 \theta ) \sin ( 3 \theta )$ 
A)  $2 \cos ( 3 \theta )$ 
B)  $2 \cos ( 7 \theta ) \cos ( 3 \theta )$ 
C)  $- 2 \sin ( 7 \theta ) \sin ( 3 \theta )$ 
D)  $- 2 \cos ( 7 \theta ) \sin ( 3 \theta )$

Question 20

Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$\csc ( 2 \theta ) + \cot ( 2 \theta ) =$ ?

Accepted Answer

A)  $\tan \theta$ 
B)  $\tan \frac { \theta } { 2 }$ 
C)  $\cot \frac { \theta } { 2 }$ 
D)  $\cot \theta$ 
A)  $\tan \theta$ 
B)  $\tan \frac { \theta } { 2 }$ 
C)  $\cot \frac { \theta } { 2 }$ 
D)  $\cot \theta$

Find the inverse function f-1 of the function f. - $f ( x ) = - \sin ( x + 6 ) - 5$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\sec ^ { 4 } \theta + \sec ^ { 2 } \theta \tan ^ { 2 } \theta - 2 \tan ^ { 4 } \theta =$ ?

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\cos \left( x + \frac { \pi } { 6 } \right) = \frac { \sqrt { 3 } } { 2 } \cos x - \frac { 1 } { 2 } \sin x$

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

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\tan \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$

Find the exact value under the given conditions. - $\cos \alpha = - \frac { 5 } { 13 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = \frac { 8 } { 17 } , \frac { \pi } { 2 } < \alpha < \pi \quad$ Find $\tan ( \alpha - \beta ) .$

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

Write the trigonometric expression as an algebraic expression in u. - $\sin \left( \tan ^ { - 1 } u \right)$

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

Find the exact value under the given conditions. - $\sin \alpha = \frac { 20 } { 29 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \cos \beta = \frac { 3 } { 5 } , 0 < \beta < \frac { \pi } { 2 } \quad$ Find $\sin ( \alpha - \beta )$ .

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

Choose the one alternative that best completes the statement or answers the question. - $\cos ^ { 2 } x + \cos x - 1 = 0$

Solve the problem. -If $\tan \theta = \frac { 7 } { 24 }$ , and $\theta$ terminates in quadrant III, then find $\cos 2 \theta$ .

Choose the one alternative that best completes the statement or answers the question. Express the product as a sum containing only sines or cosines. - $\cos ( 5 \theta ) \cos ( 4 \theta )$

Simplify the expression. - $4 \sin \theta \cos ^ { 3 } \theta - 4 \sin ^ { 3 } \theta \cos \theta$

Express the sum or difference as a product of sines and/or cosines. - $\cos ( 10 \theta ) - \cos ( 4 \theta )$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\csc ( 2 \theta ) + \cot ( 2 \theta ) =$ ?

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 inverse function f-1 of the function f. - f(x)=−sin⁡(x+6)−5f ( x ) = - \sin ( x + 6 ) - 5f(x)=−sin(x+6)−5

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - sec⁡4θ+sec⁡2θtan⁡2θ−2tan⁡4θ=\sec ^ { 4 } \theta + \sec ^ { 2 } \theta \tan ^ { 2 } \theta - 2 \tan ^ { 4 } \theta =sec4θ+sec2θtan2θ−2tan4θ= ?

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - cos⁡(x+π6)=32cos⁡x−12sin⁡x\cos \left( x + \frac { \pi } { 6 } \right) = \frac { \sqrt { 3 } } { 2 } \cos x - \frac { 1 } { 2 } \sin xcos(x+6π​)=23​​cosx−21​sinx

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - tan⁡(sin⁡−122)\tan \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)tan(sin−122​​)

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - sin⁡2θ+sin⁡2θcot⁡2θ=\sin ^ { 2 } \theta + \sin ^ { 2 } \theta \cot ^ { 2 } \theta =sin2θ+sin2θcot2θ= ?

Write the trigonometric expression as an algebraic expression in u. - sin⁡(tan⁡−1u)\sin \left( \tan ^ { - 1 } u \right)sin(tan−1u)

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - tan⁡(cos⁡−113)\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)tan(cos−131​)

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

Choose the one alternative that best completes the statement or answers the question. - cos⁡2x+cos⁡x−1=0\cos ^ { 2 } x + \cos x - 1 = 0cos2x+cosx−1=0

Solve the problem. -If tan⁡θ=724\tan \theta = \frac { 7 } { 24 }tanθ=247​ , and θ\thetaθ terminates in quadrant III, then find cos⁡2θ\cos 2 \thetacos2θ .

Choose the one alternative that best completes the statement or answers the question. Express the product as a sum containing only sines or cosines. - cos⁡(5θ)cos⁡(4θ)\cos ( 5 \theta ) \cos ( 4 \theta )cos(5θ)cos(4θ)

Simplify the expression. - 4sin⁡θcos⁡3θ−4sin⁡3θcos⁡θ4 \sin \theta \cos ^ { 3 } \theta - 4 \sin ^ { 3 } \theta \cos \theta4sinθcos3θ−4sin3θcosθ

Express the sum or difference as a product of sines and/or cosines. - cos⁡(10θ)−cos⁡(4θ)\cos ( 10 \theta ) - \cos ( 4 \theta )cos(10θ)−cos(4θ)

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - csc⁡(2θ)+cot⁡(2θ)=\csc ( 2 \theta ) + \cot ( 2 \theta ) =csc(2θ)+cot(2θ)= ?

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 inverse function f-1 of the function f. - $f ( x ) = - \sin ( x + 6 ) - 5$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\sec ^ { 4 } \theta + \sec ^ { 2 } \theta \tan ^ { 2 } \theta - 2 \tan ^ { 4 } \theta =$ ?

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\cos \left( x + \frac { \pi } { 6 } \right) = \frac { \sqrt { 3 } } { 2 } \cos x - \frac { 1 } { 2 } \sin x$

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\tan \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$

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

Write the trigonometric expression as an algebraic expression in u. - $\sin \left( \tan ^ { - 1 } u \right)$

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

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

Choose the one alternative that best completes the statement or answers the question. - $\cos ^ { 2 } x + \cos x - 1 = 0$

Solve the problem. -If $\tan \theta = \frac { 7 } { 24 }$ , and $\theta$ terminates in quadrant III, then find $\cos 2 \theta$ .

Choose the one alternative that best completes the statement or answers the question. Express the product as a sum containing only sines or cosines. - $\cos ( 5 \theta ) \cos ( 4 \theta )$

Simplify the expression. - $4 \sin \theta \cos ^ { 3 } \theta - 4 \sin ^ { 3 } \theta \cos \theta$

Express the sum or difference as a product of sines and/or cosines. - $\cos ( 10 \theta ) - \cos ( 4 \theta )$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\csc ( 2 \theta ) + \cot ( 2 \theta ) =$ ?