Question 1

Write the word or phrase that best completes each statement or answers the question.
-$$\cos ^ { 4 } x = \frac { 1 } { 8 } ( 3 + 4 \cos 2 x + \cos 4 x )$$

Accepted Answer

\[\begin{array} { l } 
\cos ^ { 4 } x =

Question 2

Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
-$$\cot x \sec ^ { 4 } x = \cot x + 2 \tan x + \tan ^ { 3 } x$$

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.
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 $i ^ { \circ }$ 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 Flagstaff, Arizona, ( $35 ^ { \circ } 13 ^ { \prime }$ north latitude) for summer solstice $\left( \mathrm { i } = 23.5 ^ { \circ } \right)$. orth

Accepted Answer

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

Question 4

Solve the problem using Snell's Law: $$\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }$$
-The index of refraction of light passing from air into a second medium is $1.67$. If the angle of incidence is $87 ^ { \circ }$, what is the angle of refraction (to two decimal places)?

Accepted Answer

A)  $54.31 ^ { \circ }$ 
B)  $53.27 ^ { \circ }$ 
C)  $36.73 ^ { \circ }$ 
D)  $35.69 ^ { \circ }$ 
A)  $54.31 ^ { \circ }$ 
B)  $53.27 ^ { \circ }$ 
C)  $36.73 ^ { \circ }$ 
D)  $35.69 ^ { \circ }$

Question 5

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The ground movement of an earthquake near a fault line is modeled by the equation
$$\mathrm { d } = \mathrm { D } \tan \left[ \frac { \pi } { 2 } \left( 1 - \frac { 2 \mathrm { M } } { \mathrm { S } } \right) \right]$$
where $\mathrm { M }$ is the horizontal movement (in meters) at a distance $\mathrm { d }$ (in kilometers) from the earthquake, $\mathrm { D }$ is the dep in kilometers) below the surface of the center of the earthquake, and $\mathrm { S }$ is the total horizontal displacement (also in meters) at the fault line. What is the horizontal movement 5 kilometers from an earthquake centered 3 kilometers the surface with a total horizontal displacement of 4 meters? Round the answer to the nearest $0.01$ meter.

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.
Complete the identity.
-$$1 - \frac { 1 } { 2 } \sin ( 2 \theta ) = ?$$

Accepted Answer

A)  $\frac { \sin \theta \cos ( 2 \theta ) } { \sin \theta + \cos \theta }$ 
B)  $\frac { \sin ^ { 3 } \theta + \cos ^ { 3 } \theta } { \sin \theta + \cos \theta }$ 
C)  $\frac { \sin ^ { 3 } \theta - \cos ^ { 3 } \theta } { \sin \theta + \cos \theta }$ 
D)  $\frac { \sin \theta \cos \theta \cos ( 2 \theta ) } { \sin \theta + \cos \theta }$ 
A)  $\frac { \sin \theta \cos ( 2 \theta ) } { \sin \theta + \cos \theta }$ 
B)  $\frac { \sin ^ { 3 } \theta + \cos ^ { 3 } \theta } { \sin \theta + \cos \theta }$ 
C)  $\frac { \sin ^ { 3 } \theta - \cos ^ { 3 } \theta } { \sin \theta + \cos \theta }$ 
D)  $\frac { \sin \theta \cos \theta \cos ( 2 \theta ) } { \sin \theta + \cos \theta }$

Question 7

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

Accepted Answer

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

Question 8

Use a calculator to find the value of the expression in radian measure rounded to two decimal places.
-$\sec ^ { - 1 } \left( - \frac { 7 } { 3 } \right)$

Accepted Answer

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

Question 9

Complete the identity.
-$\frac { \cos ( 3 \theta ) - \cos ( 9 \theta ) } { \cos ( 3 \theta ) + \cos ( 9 \theta ) } = ?$

Accepted Answer

A)  0 
B)  $\tan ( 3 \theta ) \tan ( 6 \theta )$ 
C)  $\cot ( 6 \theta )$ 
D)  $- \tan ( 6 \theta )$ 
A)  0 
B)  $\tan ( 3 \theta ) \tan ( 6 \theta )$ 
C)  $\cot ( 6 \theta )$ 
D)  $- \tan ( 6 \theta )$

Question 10

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

Accepted Answer

\[\begin{array} { l } 
( \sin x ) ( \tan

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Find $\cos \theta$, given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in quadrant I.

Accepted Answer

A)  $\frac { \sqrt { 8 - 2 \sqrt { 10 } } } { 4 }$ 
B)  $\frac { \sqrt { 6 } } { 4 }$ 
C)  $\frac { \sqrt { 10 } } { 4 }$ 
D)  $\frac { \sqrt { 8 - 2 \sqrt { 5 } } } { 2 }$ 
A)  $\frac { \sqrt { 8 - 2 \sqrt { 10 } } } { 4 }$ 
B)  $\frac { \sqrt { 6 } } { 4 }$ 
C)  $\frac { \sqrt { 10 } } { 4 }$ 
D)  $\frac { \sqrt { 8 - 2 \sqrt { 5 } } } { 2 }$

Question 12

Find the inverse function f-1 of the function f.
-$$f ( x ) = - 7 \cos ( 4 x )$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 4 } \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 7 } \right)$ 
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)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 4 } \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 7 } \right)$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 4 } \cos ^ { - 1 } \left( \frac { \mathrm { x } } { 7 } \right)$ 
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 13

Solve the problem using Snell's Law: $$\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }$$
-A light beam in air travels at $2.99 \times 10 ^ { 8 }$ meters per second. If its angle of incidence to a second medium is $77 ^ { \circ }$ and its angle of refraction in the second medium is $67 ^ { \circ }$, what is its speed in the second medium (to two decimal places)?

Accepted Answer

A)  $2.91 \times 10 ^ { 8 } \mathrm { mps }$ 
B)  $3.16 \times 10 ^ { 8 } \mathrm { mps }$ 
C)  $2.82 \times 10 ^ { 8 } \mathrm { mps }$ 
D)  $2.75 \times 10 ^ { 8 } \mathrm { mps }$ 
A)  $2.91 \times 10 ^ { 8 } \mathrm { mps }$ 
B)  $3.16 \times 10 ^ { 8 } \mathrm { mps }$ 
C)  $2.82 \times 10 ^ { 8 } \mathrm { mps }$ 
D)  $2.75 \times 10 ^ { 8 } \mathrm { mps }$

Question 14

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

Accepted Answer

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

Question 15

Solve the problem using Snell's Law: $$\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }$$
-A light beam traveling through air makes an angle of incidence of $39 ^ { \circ }$ upon a second medium. The refracted beam makes an angle of refraction of $28 ^ { \circ }$. What is the index of refraction of the material of the second medium? Give the answer to two decimal places.

Accepted Answer

A)  $0.47$ 
B)  $0.75$ 
C)  $0.63$ 
D)  $1.34$ 
A)  $0.47$ 
B)  $0.75$ 
C)  $0.63$ 
D)  $1.34$

Question 16

Solve the equation. Give a general formula for all the solutions.
-$$\cos ( 2 \theta ) = \frac { \sqrt { 2 } } { 2 }$$

Accepted Answer

A)  $\theta = \frac { \pi } { 8 } + 2 \mathrm { k } \pi , \theta = \frac { 7 \pi } { 8 } + 2 \mathrm { k } \pi$ 
B)  $\theta = \frac { 2 \pi } { 3 } + \mathrm { k } \pi , \theta = \frac { 4 \pi } { 3 } + \mathrm { k } \pi$ 
C)  $\theta = \frac { \pi } { 4 } + \mathrm { k } \pi , \theta = \frac { 3 \pi } { 4 } + \mathrm { k } \pi$ 
D)  $\theta = \frac { \pi } { 8 } + \mathrm { k } \pi , \theta = \frac { 7 \pi } { 8 } + \mathrm { k } \pi$ 
A)  $\theta = \frac { \pi } { 8 } + 2 \mathrm { k } \pi , \theta = \frac { 7 \pi } { 8 } + 2 \mathrm { k } \pi$ 
B)  $\theta = \frac { 2 \pi } { 3 } + \mathrm { k } \pi , \theta = \frac { 4 \pi } { 3 } + \mathrm { k } \pi$ 
C)  $\theta = \frac { \pi } { 4 } + \mathrm { k } \pi , \theta = \frac { 3 \pi } { 4 } + \mathrm { k } \pi$ 
D)  $\theta = \frac { \pi } { 8 } + \mathrm { k } \pi , \theta = \frac { 7 \pi } { 8 } + \mathrm { k } \pi$

Question 17

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

Accepted Answer

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

Question 18

Solve the equation. Give a general formula for all the solutions.
-$$\csc \frac { \theta } { 3 } = \frac { 2 \sqrt { 3 } } { 3 }$$

Accepted Answer

A)  $\theta = \frac { \pi } { 3 } + 2 \mathrm { k } \pi , \theta = \frac { \pi } { 9 } + 2 \mathrm { k } \pi$ 
B)  $\theta = \pi + 6 \mathrm { k } \pi , \theta = 2 \pi + 6 \mathrm { k } \pi$ 
C)  $\theta = \frac { \pi } { 9 } + 2 \mathrm { k } \pi , \theta = \frac { \pi } { 18 } + 2 \mathrm { k } \pi$ 
D)  $\theta = \frac { \pi } { 2 } + 6 \mathrm { k } \pi , \theta = \pi + 6 \mathrm { k } \pi$ 
A)  $\theta = \frac { \pi } { 3 } + 2 \mathrm { k } \pi , \theta = \frac { \pi } { 9 } + 2 \mathrm { k } \pi$ 
B)  $\theta = \pi + 6 \mathrm { k } \pi , \theta = 2 \pi + 6 \mathrm { k } \pi$ 
C)  $\theta = \frac { \pi } { 9 } + 2 \mathrm { k } \pi , \theta = \frac { \pi } { 18 } + 2 \mathrm { k } \pi$ 
D)  $\theta = \frac { \pi } { 2 } + 6 \mathrm { k } \pi , \theta = \pi + 6 \mathrm { k } \pi$

Question 19

Find the exact value of the expression.
-$$\frac { 1 - \tan 80 ^ { \circ } \tan 70 ^ { \circ } } { \tan 80 ^ { \circ } + \tan 70 ^ { \circ } }$$

Accepted Answer

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

Question 20

Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
-$$\sin ^ { 3 } x \cos ^ { 2 } x = \sin x \left( \cos ^ { 2 } x - \cos ^ { 4 } x \right)$$

Accepted Answer

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

Write the word or phrase that best completes each statement or answers the question. - $\cos ^ { 4 } x = \frac { 1 } { 8 } ( 3 + 4 \cos 2 x + \cos 4 x )$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\cot x \sec ^ { 4 } x = \cot x + 2 \tan x + \tan ^ { 3 } x$

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

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

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. - $\sec ^ { - 1 } \left( - \frac { 7 } { 3 } \right)$

Complete the identity. - $\frac { \cos ( 3 \theta ) - \cos ( 9 \theta ) } { \cos ( 3 \theta ) + \cos ( 9 \theta ) } = ?$

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

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find $\cos \theta$ , given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in quadrant I.

Find the inverse function f-1 of the function f. - $f ( x ) = - 7 \cos ( 4 x )$

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

Solve the equation. Give a general formula for all the solutions. - $\cos ( 2 \theta ) = \frac { \sqrt { 2 } } { 2 }$

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

Solve the equation. Give a general formula for all the solutions. - $\csc \frac { \theta } { 3 } = \frac { 2 \sqrt { 3 } } { 3 }$

Find the exact value of the expression. - $\frac { 1 - \tan 80 ^ { \circ } \tan 70 ^ { \circ } } { \tan 80 ^ { \circ } + \tan 70 ^ { \circ } }$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\sin ^ { 3 } x \cos ^ { 2 } x = \sin x \left( \cos ^ { 2 } x - \cos ^ { 4 } x \right)$

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

Write the word or phrase that best completes each statement or answers the question. - cos⁡4x=18(3+4cos⁡2x+cos⁡4x)\cos ^ { 4 } x = \frac { 1 } { 8 } ( 3 + 4 \cos 2 x + \cos 4 x )cos4x=81​(3+4cos2x+cos4x)

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - cot⁡xsec⁡4x=cot⁡x+2tan⁡x+tan⁡3x\cot x \sec ^ { 4 } x = \cot x + 2 \tan x + \tan ^ { 3 } xcotxsec4x=cotx+2tanx+tan3x

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - 1−12sin⁡(2θ)=?1 - \frac { 1 } { 2 } \sin ( 2 \theta ) = ?1−21​sin(2θ)=?

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

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. - sec⁡−1(−73)\sec ^ { - 1 } \left( - \frac { 7 } { 3 } \right)sec−1(−37​)

Complete the identity. - cos⁡(3θ)−cos⁡(9θ)cos⁡(3θ)+cos⁡(9θ)=?\frac { \cos ( 3 \theta ) - \cos ( 9 \theta ) } { \cos ( 3 \theta ) + \cos ( 9 \theta ) } = ?cos(3θ)+cos(9θ)cos(3θ)−cos(9θ)​=?

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - (sin⁡x)(tan⁡xcos⁡x−cot⁡xcos⁡x)=1−2cos⁡2x( \sin x ) ( \tan x \cos x - \cot x \cos x ) = 1 - 2 \cos ^ { 2 } x(sinx)(tanxcosx−cotxcosx)=1−2cos2x

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find cos⁡θ\cos \thetacosθ , given that cos⁡2θ=14\cos 2 \theta = \frac { 1 } { 4 }cos2θ=41​ and θ\thetaθ terminates in quadrant I.

Find the inverse function f-1 of the function f. - f(x)=−7cos⁡(4x)f ( x ) = - 7 \cos ( 4 x )f(x)=−7cos(4x)

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

Solve the equation. Give a general formula for all the solutions. - cos⁡(2θ)=22\cos ( 2 \theta ) = \frac { \sqrt { 2 } } { 2 }cos(2θ)=22​​

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

Solve the equation. Give a general formula for all the solutions. - csc⁡θ3=233\csc \frac { \theta } { 3 } = \frac { 2 \sqrt { 3 } } { 3 }csc3θ​=323​​

Find the exact value of the expression. - 1−tan⁡80∘tan⁡70∘tan⁡80∘+tan⁡70∘\frac { 1 - \tan 80 ^ { \circ } \tan 70 ^ { \circ } } { \tan 80 ^ { \circ } + \tan 70 ^ { \circ } }tan80∘+tan70∘1−tan80∘tan70∘​

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - sin⁡3xcos⁡2x=sin⁡x(cos⁡2x−cos⁡4x)\sin ^ { 3 } x \cos ^ { 2 } x = \sin x \left( \cos ^ { 2 } x - \cos ^ { 4 } x \right)sin3xcos2x=sinx(cos2x−cos4x)

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

Write the word or phrase that best completes each statement or answers the question. - $\cos ^ { 4 } x = \frac { 1 } { 8 } ( 3 + 4 \cos 2 x + \cos 4 x )$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\cot x \sec ^ { 4 } x = \cot x + 2 \tan x + \tan ^ { 3 } x$

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

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

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. - $\sec ^ { - 1 } \left( - \frac { 7 } { 3 } \right)$

Complete the identity. - $\frac { \cos ( 3 \theta ) - \cos ( 9 \theta ) } { \cos ( 3 \theta ) + \cos ( 9 \theta ) } = ?$

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

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find $\cos \theta$ , given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in quadrant I.

Find the inverse function f-1 of the function f. - $f ( x ) = - 7 \cos ( 4 x )$

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

Solve the equation. Give a general formula for all the solutions. - $\cos ( 2 \theta ) = \frac { \sqrt { 2 } } { 2 }$

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

Solve the equation. Give a general formula for all the solutions. - $\csc \frac { \theta } { 3 } = \frac { 2 \sqrt { 3 } } { 3 }$

Find the exact value of the expression. - $\frac { 1 - \tan 80 ^ { \circ } \tan 70 ^ { \circ } } { \tan 80 ^ { \circ } + \tan 70 ^ { \circ } }$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\sin ^ { 3 } x \cos ^ { 2 } x = \sin x \left( \cos ^ { 2 } x - \cos ^ { 4 } x \right)$