Exam 5: Trigonometric Functions

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. - $r = 9$ feet, $A = 39$ square feet, $\theta =$ ?

(Multiple Choice)

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Question 301

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $112.56 ^ { \circ }$

(Multiple Choice)

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Question 302

Solve the problem. -If $\tan \theta = - 0.4$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

(Multiple Choice)

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Question 303

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 40 ^ { \circ } \cot 40 ^ { \circ }$

(Multiple Choice)

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Question 304

Find the exact value of the expression. Do not use a calculator. - $\cos 60 ^ { \circ } + \tan 60 ^ { \circ }$

(Multiple Choice)

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Question 305

Use transformations to graph the function. - $y=4 \cos x$ $Use transformations to graph the function. - y=4 \cos x$

(Multiple Choice)

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Question 306

Name the quadrant in which the angle θ lies. - $\cot \theta < 0 , \quad \cos \theta > 0$

(Multiple Choice)

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Question 307

Find an equation for the graph. -

(Multiple Choice)

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Question 308

Draw the angle. - $\frac { 2 \pi } { 3 }$

(Multiple Choice)

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Question 309

Use transformations to graph the function. - $y=5 \cos (\pi-x)$ $Use transformations to graph the function. - y=5 \cos (\pi-x)$

(Multiple Choice)

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Question 310

Use transformations to graph the function. - $y=\cos x-1$ $Use transformations to graph the function. - y=\cos x-1$

(Multiple Choice)

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Question 311

Find the exact value. Do not use a calculator. - $\tan 60 ^ { \circ }$

(Multiple Choice)

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Question 312

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. - $\left( - \frac { \sqrt { 39 } } { 8 } , \frac { 5 } { 8 } \right) \quad$ Find $\cos t$

(Multiple Choice)

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(57)

Question 313

Graph the function. - $y = \csc \left( \frac { 1 } { 4 } x \right)$ $Graph the function. - y = \csc \left( \frac { 1 } { 4 } x \right)$

(Multiple Choice)

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(81)

Question 314

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - 30 ^ { \circ } \right)$

(Multiple Choice)

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(89)

Question 315

Solve the problem. -The blade of a windshield wiper sweeps out an angle of $135 ^ { \circ }$ in one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle? (Round to the nearest $0.1$ square inch.)

(Multiple Choice)

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(70)

Question 316

Find the length s. Round the answer to three decimal places. -

(Multiple Choice)

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(77)

Question 317

Find the exact value. Do not use a calculator. - $\cos \pi$

(Multiple Choice)

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(77)

Question 318

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. - $\left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad$ Find $\sin t$

(Multiple Choice)

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(81)

Question 319

Find the exact value of the expression. Do not use a calculator. - $\tan 150 ^ { \circ } \cos 210 ^ { \circ }$

(Multiple Choice)

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Question 320

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. - $r = 9$ feet, $A = 39$ square feet, $\theta =$ ?

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $112.56 ^ { \circ }$

Solve the problem. -If $\tan \theta = - 0.4$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 40 ^ { \circ } \cot 40 ^ { \circ }$

Find the exact value of the expression. Do not use a calculator. - $\cos 60 ^ { \circ } + \tan 60 ^ { \circ }$

Use transformations to graph the function. - $y=4 \cos x$ $Use transformations to graph the function. - y=4 \cos x$

Name the quadrant in which the angle θ lies. - $\cot \theta < 0 , \quad \cos \theta > 0$

Find an equation for the graph. -

Draw the angle. - $\frac { 2 \pi } { 3 }$

Use transformations to graph the function. - $y=5 \cos (\pi-x)$ $Use transformations to graph the function. - y=5 \cos (\pi-x)$

Use transformations to graph the function. - $y=\cos x-1$ $Use transformations to graph the function. - y=\cos x-1$

Find the exact value. Do not use a calculator. - $\tan 60 ^ { \circ }$

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. - $\left( - \frac { \sqrt { 39 } } { 8 } , \frac { 5 } { 8 } \right) \quad$ Find $\cos t$

Graph the function. - $y = \csc \left( \frac { 1 } { 4 } x \right)$ $Graph the function. - y = \csc \left( \frac { 1 } { 4 } x \right)$

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - 30 ^ { \circ } \right)$

Solve the problem. -The blade of a windshield wiper sweeps out an angle of $135 ^ { \circ }$ in one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle? (Round to the nearest $0.1$ square inch.)

Find the length s. Round the answer to three decimal places. -

Find the exact value. Do not use a calculator. - $\cos \pi$

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. - $\left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad$ Find $\sin t$

Find the exact value of the expression. Do not use a calculator. - $\tan 150 ^ { \circ } \cos 210 ^ { \circ }$

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

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=9r = 9r=9 feet, A=39A = 39A=39 square feet, θ=\theta =θ= ?

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - 112.56∘112.56 ^ { \circ }112.56∘

Solve the problem. -If tan⁡θ=−0.4\tan \theta = - 0.4tanθ=−0.4 , find the value of tan⁡θ+tan⁡(θ+π)+tan⁡(θ+2π)\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )tanθ+tan(θ+π)+tan(θ+2π) .

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - tan⁡40∘cot⁡40∘\tan 40 ^ { \circ } \cot 40 ^ { \circ }tan40∘cot40∘

Find the exact value of the expression. Do not use a calculator. - cos⁡60∘+tan⁡60∘\cos 60 ^ { \circ } + \tan 60 ^ { \circ }cos60∘+tan60∘

Use transformations to graph the function. - y=4cos⁡xy=4 \cos xy=4cosx

Name the quadrant in which the angle θ lies. - cot⁡θ<0,cos⁡θ>0\cot \theta < 0 , \quad \cos \theta > 0cotθ<0,cosθ>0

Find an equation for the graph. -

Draw the angle. - 2π3\frac { 2 \pi } { 3 }32π​

Use transformations to graph the function. - y=5cos⁡(π−x)y=5 \cos (\pi-x)y=5cos(π−x)

Use transformations to graph the function. - y=cos⁡x−1y=\cos x-1y=cosx−1

Find the exact value. Do not use a calculator. - tan⁡60∘\tan 60 ^ { \circ }tan60∘

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. - (−398,58)\left( - \frac { \sqrt { 39 } } { 8 } , \frac { 5 } { 8 } \right) \quad(−839​​,85​) Find cos⁡t\cos tcost

Graph the function. - y=csc⁡(14x)y = \csc \left( \frac { 1 } { 4 } x \right)y=csc(41​x)

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - csc⁡(−30∘)\csc \left( - 30 ^ { \circ } \right)csc(−30∘)

Find the length s. Round the answer to three decimal places. -

Find the exact value. Do not use a calculator. - cos⁡π\cos \picosπ

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. - (29,779)\left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad(92​,977​​) Find sin⁡t\sin tsint

Find the exact value of the expression. Do not use a calculator. - tan⁡150∘cos⁡210∘\tan 150 ^ { \circ } \cos 210 ^ { \circ }tan150∘cos210∘

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

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. - $r = 9$ feet, $A = 39$ square feet, $\theta =$ ?

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $112.56 ^ { \circ }$

Solve the problem. -If $\tan \theta = - 0.4$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 40 ^ { \circ } \cot 40 ^ { \circ }$

Find the exact value of the expression. Do not use a calculator. - $\cos 60 ^ { \circ } + \tan 60 ^ { \circ }$

Use transformations to graph the function. - $y=4 \cos x$ $Use transformations to graph the function. - y=4 \cos x$

Name the quadrant in which the angle θ lies. - $\cot \theta < 0 , \quad \cos \theta > 0$

Draw the angle. - $\frac { 2 \pi } { 3 }$

Use transformations to graph the function. - $y=5 \cos (\pi-x)$ $Use transformations to graph the function. - y=5 \cos (\pi-x)$

Use transformations to graph the function. - $y=\cos x-1$ $Use transformations to graph the function. - y=\cos x-1$

Find the exact value. Do not use a calculator. - $\tan 60 ^ { \circ }$

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. - $\left( - \frac { \sqrt { 39 } } { 8 } , \frac { 5 } { 8 } \right) \quad$ Find $\cos t$

Graph the function. - $y = \csc \left( \frac { 1 } { 4 } x \right)$ $Graph the function. - y = \csc \left( \frac { 1 } { 4 } x \right)$

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - 30 ^ { \circ } \right)$

Find the exact value. Do not use a calculator. - $\cos \pi$

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. - $\left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad$ Find $\sin t$

Find the exact value of the expression. Do not use a calculator. - $\tan 150 ^ { \circ } \cos 210 ^ { \circ }$