Exam 4: Trigonometric Functions

Solve the problem. -The number of hours of darkness in a coastal town can be modeled by $\mathrm { f } ( \mathrm { x } ) = 6.3 \cos \left( \frac { \pi } { 6 } ( \mathrm { x } - 2 ) \right) + 12.0$ , where $x$ is the month and $x = 1$ corresponds to January. Approximate the number of hours of darkness in April, to the nearest tenth of an hour.

(Multiple Choice)

4.9/5

(71)

Question 421

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is $27 ^ { \circ } 5 ^ { \prime }$ . If the base of the cliff is 2386 feet from the boat, how high is the cliff (to the nearest foot)?

(Multiple Choice)

4.9/5

(100)

Question 422

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $- 205 ^ { \circ }$

(Multiple Choice)

4.9/5

(81)

Question 423

Find the specified quantity. -Find the phase shift of $y = 2 - 2 \sin \left( 5 x - \frac { \pi } { 3 } \right)$ .

(Multiple Choice)

4.7/5

(88)

Question 424

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan 253 ^ { \circ }$

(Multiple Choice)

4.9/5

(69)

Question 425

Graph the function. -y = -tan 4x

(Multiple Choice)

4.8/5

(90)

Question 426

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - $\tan ^ { - 1 } ( - 1.1617 )$

(Multiple Choice)

4.8/5

(90)

Question 427

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\sin \left( - 450 ^ { \circ } \right)$

(Multiple Choice)

4.9/5

(68)

Question 428

$\text { Explain why the equation } \cos ^ { - 1 } \left( \cos \left( \frac { 5 \pi } { 4 } \right) \right) = \frac { 3 \pi } { 4 } \text { does not violate the Inverse Composition Rule. }$

(Essay)

4.8/5

(86)

Question 429

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. -y = 2 tan x

(Multiple Choice)

4.7/5

(72)

Question 430

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $55 ^ { \circ } 53 ^ { \prime } 7 ^ { \prime \prime }$

(Multiple Choice)

4.9/5

(71)

Question 431

Find the angle in degrees that describes the compass bearing. -SSE

(Multiple Choice)

4.8/5

(78)

Question 432

Give the exact value. - $\cot 45 ^ { \circ }$

(Multiple Choice)

4.8/5

(84)

Question 433

Match the function with its graph. -1) $y = - \tan \left( x - \frac { \pi } { 2 } \right)$ 2) $y = \tan \left( x + \frac { \pi } { 2 } \right)$ 3) $y = - \cot \left( x - \frac { \pi } { 2 } \right)$ 4) $y = \cot \left( x + \frac { \pi } { 2 } \right)$ a. $Match the function with its graph. -1) y = - \tan \left( x - \frac { \pi } { 2 } \right) 2) y = \tan \left( x + \frac { \pi } { 2 } \right) 3) y = - \cot \left( x - \frac { \pi } { 2 } \right) 4) y = \cot \left( x + \frac { \pi } { 2 } \right) a. b. c. d.$ b. $Match the function with its graph. -1) y = - \tan \left( x - \frac { \pi } { 2 } \right) 2) y = \tan \left( x + \frac { \pi } { 2 } \right) 3) y = - \cot \left( x - \frac { \pi } { 2 } \right) 4) y = \cot \left( x + \frac { \pi } { 2 } \right) a. b. c. d.$ c. $Match the function with its graph. -1) y = - \tan \left( x - \frac { \pi } { 2 } \right) 2) y = \tan \left( x + \frac { \pi } { 2 } \right) 3) y = - \cot \left( x - \frac { \pi } { 2 } \right) 4) y = \cot \left( x + \frac { \pi } { 2 } \right) a. b. c. d.$ d. $Match the function with its graph. -1) y = - \tan \left( x - \frac { \pi } { 2 } \right) 2) y = \tan \left( x + \frac { \pi } { 2 } \right) 3) y = - \cot \left( x - \frac { \pi } { 2 } \right) 4) y = \cot \left( x + \frac { \pi } { 2 } \right) a. b. c. d.$

(Multiple Choice)

4.8/5

(87)

Question 434

Graph the function. - $y=\frac{1}{3} \sin \frac{1}{4} x$ $Graph the function. - y=\frac{1}{3} \sin \frac{1}{4} x$

(Multiple Choice)

4.9/5

(81)

Question 435

Give the exact value. - $\cos \frac { \pi } { 6 }$

(Multiple Choice)

5.0/5

(83)

Question 436

Find the trigonometric function value for the angle shown. - $\cos \theta$ $Find the trigonometric function value for the angle shown. - \cos \theta$

(Multiple Choice)

4.8/5

(93)

Question 437

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $45 ^ { \circ } 54 ^ { \prime } 18 ^ { \prime \prime }$

(Multiple Choice)

4.9/5

(90)

Question 438

Select the functions that have identical graphs. -(i) $y = \cos x$ (ii) $y = - \sin ( x - \pi )$ (iii) $y = \cos \left( x - \frac { \pi } { 2 } \right)$

(Multiple Choice)

4.8/5

(65)

Question 439

Find the trigonometric function value for the angle shown. - $\cos \theta$ $Find the trigonometric function value for the angle shown. - \cos \theta$

(Multiple Choice)

4.7/5

(78)

Question 440

Showing 421 - 440 of 522

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is $27 ^ { \circ } 5 ^ { \prime }$ . If the base of the cliff is 2386 feet from the boat, how high is the cliff (to the nearest foot)?

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $- 205 ^ { \circ }$

Find the specified quantity. -Find the phase shift of $y = 2 - 2 \sin \left( 5 x - \frac { \pi } { 3 } \right)$ .

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan 253 ^ { \circ }$

Graph the function. -y = -tan 4x

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - $\tan ^ { - 1 } ( - 1.1617 )$

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\sin \left( - 450 ^ { \circ } \right)$

$\text { Explain why the equation } \cos ^ { - 1 } \left( \cos \left( \frac { 5 \pi } { 4 } \right) \right) = \frac { 3 \pi } { 4 } \text { does not violate the Inverse Composition Rule. }$

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. -y = 2 tan x

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $55 ^ { \circ } 53 ^ { \prime } 7 ^ { \prime \prime }$

Find the angle in degrees that describes the compass bearing. -SSE

Give the exact value. - $\cot 45 ^ { \circ }$

Graph the function. - $y=\frac{1}{3} \sin \frac{1}{4} x$ $Graph the function. - y=\frac{1}{3} \sin \frac{1}{4} x$

Give the exact value. - $\cos \frac { \pi } { 6 }$

Find the trigonometric function value for the angle shown. - $\cos \theta$ $Find the trigonometric function value for the angle shown. - \cos \theta$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $45 ^ { \circ } 54 ^ { \prime } 18 ^ { \prime \prime }$

Select the functions that have identical graphs. -(i) $y = \cos x$ (ii) $y = - \sin ( x - \pi )$ (iii) $y = \cos \left( x - \frac { \pi } { 2 } \right)$

Find the trigonometric function value for the angle shown. - $\cos \theta$ $Find the trigonometric function value for the angle shown. - \cos \theta$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 4: Trigonometric Functions

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is 27∘5′27 ^ { \circ } 5 ^ { \prime }27∘5′ . If the base of the cliff is 2386 feet from the boat, how high is the cliff (to the nearest foot)?

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - −205∘- 205 ^ { \circ }−205∘

Find the specified quantity. -Find the phase shift of y=2−2sin⁡(5x−π3)y = 2 - 2 \sin \left( 5 x - \frac { \pi } { 3 } \right)y=2−2sin(5x−3π​) .

Determine the sign (positive or negative) of the given value without use of a calculator. - tan⁡253∘\tan 253 ^ { \circ }tan253∘

Graph the function. -y = -tan 4x

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - tan⁡−1(−1.1617)\tan ^ { - 1 } ( - 1.1617 )tan−1(−1.1617)

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - sin⁡(−450∘)\sin \left( - 450 ^ { \circ } \right)sin(−450∘)

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. -y = 2 tan x

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 55∘53′7′′55 ^ { \circ } 53 ^ { \prime } 7 ^ { \prime \prime }55∘53′7′′

Find the angle in degrees that describes the compass bearing. -SSE

Give the exact value. - cot⁡45∘\cot 45 ^ { \circ }cot45∘

Graph the function. - y=13sin⁡14xy=\frac{1}{3} \sin \frac{1}{4} xy=31​sin41​x

Give the exact value. - cos⁡π6\cos \frac { \pi } { 6 }cos6π​

Find the trigonometric function value for the angle shown. - cos⁡θ\cos \thetacosθ

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 45∘54′18′′45 ^ { \circ } 54 ^ { \prime } 18 ^ { \prime \prime }45∘54′18′′

Select the functions that have identical graphs. -(i) y=cos⁡xy = \cos xy=cosx (ii) y=−sin⁡(x−π)y = - \sin ( x - \pi )y=−sin(x−π) (iii) y=cos⁡(x−π2)y = \cos \left( x - \frac { \pi } { 2 } \right)y=cos(x−2π​)

Find the trigonometric function value for the angle shown. - cos⁡θ\cos \thetacosθ

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is $27 ^ { \circ } 5 ^ { \prime }$ . If the base of the cliff is 2386 feet from the boat, how high is the cliff (to the nearest foot)?

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $- 205 ^ { \circ }$

Find the specified quantity. -Find the phase shift of $y = 2 - 2 \sin \left( 5 x - \frac { \pi } { 3 } \right)$ .

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan 253 ^ { \circ }$

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - $\tan ^ { - 1 } ( - 1.1617 )$

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\sin \left( - 450 ^ { \circ } \right)$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $55 ^ { \circ } 53 ^ { \prime } 7 ^ { \prime \prime }$

Give the exact value. - $\cot 45 ^ { \circ }$

Graph the function. - $y=\frac{1}{3} \sin \frac{1}{4} x$ $Graph the function. - y=\frac{1}{3} \sin \frac{1}{4} x$

Give the exact value. - $\cos \frac { \pi } { 6 }$

Find the trigonometric function value for the angle shown. - $\cos \theta$ $Find the trigonometric function value for the angle shown. - \cos \theta$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $45 ^ { \circ } 54 ^ { \prime } 18 ^ { \prime \prime }$

Select the functions that have identical graphs. -(i) $y = \cos x$ (ii) $y = - \sin ( x - \pi )$ (iii) $y = \cos \left( x - \frac { \pi } { 2 } \right)$

Find the trigonometric function value for the angle shown. - $\cos \theta$ $Find the trigonometric function value for the angle shown. - \cos \theta$