Exam 5: Trigonometric Functions

Graph the sinusoidal function. - $y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)$ $Graph the sinusoidal function. - y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)$

(Multiple Choice)

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Question 261

Write the word or phrase that best completes each statement or answers the question. - $\text { Is the function } \mathrm { f } ( \theta ) = \sin \theta + \cos \theta \text { even, odd, or neither? }$

(Short Answer)

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Question 262

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 2 , - 1 )$ Find $\csc \theta$ .

(Multiple Choice)

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Question 263

Find an equation for the graph. -

(Multiple Choice)

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Question 264

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 42 ^ { \circ }$

(Multiple Choice)

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Question 265

Graph the function. - $y=\sec \left(x-\frac{\pi}{6}\right)$ $Graph the function. - y=\sec \left(x-\frac{\pi}{6}\right)$

(Multiple Choice)

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Question 266

Graph the function. Show at least one period. - $y = 5 \cos \left( 5 x + \frac { \pi } { 2 } \right)$ $Graph the function. Show at least one period. - y = 5 \cos \left( 5 x + \frac { \pi } { 2 } \right)$

(Multiple Choice)

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Question 267

Graph the function. - $y=\sec (3 x)$ $Graph the function. - y=\sec (3 x)$

(Multiple Choice)

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Question 268

Find the area A. Round the answer to three decimal places. -

(Multiple Choice)

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Question 269

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\csc 2 ^ { \circ }$

(Multiple Choice)

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Question 270

Solve the problem. -As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 120 square yards in the shape of a sector of a circle of radius 30 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places.

(Multiple Choice)

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Question 271

Draw the angle. - $- \frac { 3 \pi } { 4 }$

(Multiple Choice)

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Question 272

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $4 \pi$ Phase Shift: $\frac { \pi } { 4 }$

(Multiple Choice)

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Question 273

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 4 } { 9 } , \frac { \sqrt { 65 } } { 9 } \right) \quad$ Find tan $t$

(Multiple Choice)

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Question 274

Choose the one alternative that best completes the statement or answers the question. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\sec \theta$

(Multiple Choice)

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Question 275

Find the exact value. Do not use a calculator. - $\sin 495 ^ { \circ }$

(Multiple Choice)

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Question 276

Match the given function to its graph. -1) $y = \sin x$ 2) $y = \cos x$ 3) $y = - \sin x$ 4) $y = - \cos x$ A. $Match the given function to its graph. -1) y = \sin x 2) y = \cos x 3) y = - \sin x 4) y = - \cos x A. B. C. D.$ B. $Match the given function to its graph. -1) y = \sin x 2) y = \cos x 3) y = - \sin x 4) y = - \cos x A. B. C. D.$ C. $Match the given function to its graph. -1) y = \sin x 2) y = \cos x 3) y = - \sin x 4) y = - \cos x A. B. C. D.$ D. $Match the given function to its graph. -1) y = \sin x 2) y = \cos x 3) y = - \sin x 4) y = - \cos x A. B. C. D.$

(Multiple Choice)

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Question 277

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 3$

(Multiple Choice)

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Question 278

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\mathrm { r } = 5$ inches, $\theta = 2$ radians, $\mathrm { A } =$ ?

(Multiple Choice)

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Question 279

Solve the problem. -A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be moving when the wheels are rotating at 430 revolutions per minute? Express the answer in miles per hour Rounded to the nearest whole number.

(Multiple Choice)

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Question 280

Showing 261 - 280 of 354

Graph the sinusoidal function. - $y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)$ $Graph the sinusoidal function. - y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)$

Write the word or phrase that best completes each statement or answers the question. - $\text { Is the function } \mathrm { f } ( \theta ) = \sin \theta + \cos \theta \text { even, odd, or neither? }$

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 2 , - 1 )$ Find $\csc \theta$ .

Find an equation for the graph. -

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 42 ^ { \circ }$

Graph the function. - $y=\sec \left(x-\frac{\pi}{6}\right)$ $Graph the function. - y=\sec \left(x-\frac{\pi}{6}\right)$

Graph the function. Show at least one period. - $y = 5 \cos \left( 5 x + \frac { \pi } { 2 } \right)$ $Graph the function. Show at least one period. - y = 5 \cos \left( 5 x + \frac { \pi } { 2 } \right)$

Graph the function. - $y=\sec (3 x)$ $Graph the function. - y=\sec (3 x)$

Find the area A. Round the answer to three decimal places. -

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\csc 2 ^ { \circ }$

Draw the angle. - $- \frac { 3 \pi } { 4 }$

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $4 \pi$ Phase Shift: $\frac { \pi } { 4 }$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 4 } { 9 } , \frac { \sqrt { 65 } } { 9 } \right) \quad$ Find tan $t$

Choose the one alternative that best completes the statement or answers the question. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\sec \theta$

Find the exact value. Do not use a calculator. - $\sin 495 ^ { \circ }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 3$

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\mathrm { r } = 5$ inches, $\theta = 2$ radians, $\mathrm { A } =$ ?

Solve the problem. -A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be moving when the wheels are rotating at 430 revolutions per minute? Express the answer in miles per hour Rounded to the nearest whole number.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

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 5: Trigonometric Functions

Graph the sinusoidal function. - y=73cos⁡(−12x)y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)y=37​cos(−21​x)

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - (−2,−1)( - 2 , - 1 )(−2,−1) Find csc⁡θ\csc \thetacscθ .

Find an equation for the graph. -

Use a calculator to find the approximate value of the expression rounded to two decimal places. - tan⁡42∘\tan 42 ^ { \circ }tan42∘

Graph the function. - y=sec⁡(x−π6)y=\sec \left(x-\frac{\pi}{6}\right)y=sec(x−6π​)

Graph the function. Show at least one period. - y=5cos⁡(5x+π2)y = 5 \cos \left( 5 x + \frac { \pi } { 2 } \right)y=5cos(5x+2π​)

Graph the function. - y=sec⁡(3x)y=\sec (3 x)y=sec(3x)

Find the area A. Round the answer to three decimal places. -

Use a calculator to find the approximate value of the expression rounded to two decimal places. - csc⁡2∘\csc 2 ^ { \circ }csc2∘

Draw the angle. - −3π4- \frac { 3 \pi } { 4 }−43π​

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: 4π4 \pi4π Phase Shift: π4\frac { \pi } { 4 }4π​

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - (49,659)\left( \frac { 4 } { 9 } , \frac { \sqrt { 65 } } { 9 } \right) \quad(94​,965​​) Find tan ttt

Find the exact value. Do not use a calculator. - sin⁡495∘\sin 495 ^ { \circ }sin495∘

Match the given function to its graph. -1) y=sin⁡xy = \sin xy=sinx 2) y=cos⁡xy = \cos xy=cosx 3) y=−sin⁡xy = - \sin xy=−sinx 4) y=−cos⁡xy = - \cos xy=−cosx A. B. C. D.

Use a calculator to find the approximate value of the expression rounded to two decimal places. - cos⁡3\cos 3cos3

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - r=5\mathrm { r } = 5r=5 inches, θ=2\theta = 2θ=2 radians, A=\mathrm { A } =A= ?

Solve the problem. -A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be moving when the wheels are rotating at 430 revolutions per minute? Express the answer in miles per hour Rounded to the nearest whole number.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

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

Graph the sinusoidal function. - $y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)$ $Graph the sinusoidal function. - y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)$

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 2 , - 1 )$ Find $\csc \theta$ .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 42 ^ { \circ }$

Graph the function. - $y=\sec \left(x-\frac{\pi}{6}\right)$ $Graph the function. - y=\sec \left(x-\frac{\pi}{6}\right)$

Graph the function. Show at least one period. - $y = 5 \cos \left( 5 x + \frac { \pi } { 2 } \right)$ $Graph the function. Show at least one period. - y = 5 \cos \left( 5 x + \frac { \pi } { 2 } \right)$

Graph the function. - $y=\sec (3 x)$ $Graph the function. - y=\sec (3 x)$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\csc 2 ^ { \circ }$

Draw the angle. - $- \frac { 3 \pi } { 4 }$

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $4 \pi$ Phase Shift: $\frac { \pi } { 4 }$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 4 } { 9 } , \frac { \sqrt { 65 } } { 9 } \right) \quad$ Find tan $t$

Find the exact value. Do not use a calculator. - $\sin 495 ^ { \circ }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 3$

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\mathrm { r } = 5$ inches, $\theta = 2$ radians, $\mathrm { A } =$ ?