Exam 5: Trigonometric Functions

Solve the problem. -A weight hangs from a rope 20 feet long. It swings through an angle of $27 ^ { \circ }$ each second. How far does the weight travel each second? Round to the nearest $0.1$ foot.

(Multiple Choice)

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Question 61

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 P of the mass at time t is given by $P = 4 \cos ( 4 t )$ What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0. $Write the word or phrase that best completes each statement or answers the question. -A mass hangs from a spring which oscillates up and down. The position P of the mass at time t is given by P = 4 \cos ( 4 t ) What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0.$

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Question 62

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

(Multiple Choice)

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Question 63

Graph the function. - $y=-\cot x$ $Graph the function. - y=-\cot x$

(Multiple Choice)

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Question 64

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=\sin x-2$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=\sin x-2$

(Multiple Choice)

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Question 65

Write the word or phrase that best completes each statement or answers the question. -Determine the sign of the trigonometric values listed below. (i) $\sin 250 ^ { \circ }$ (ii) $\tan 330 ^ { \circ }$ (iii) $\cos \left( - 40 ^ { \circ } \right)$

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Question 66

Graph the function. - $y=-\cot (2 x)$ $Graph the function. - y=-\cot (2 x)$

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Question 67

Solve the problem. -If $f ( \theta ) = \cos \theta$ and $f ( a ) = - \frac { 1 } { 12 }$ , find the exact value of $f ( a ) + f ( a - 2 \pi ) + f ( a + 4 \pi )$ .

(Multiple Choice)

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Question 68

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

(Multiple Choice)

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Question 69

Solve the problem. -What is the range of the tangent function?

(Multiple Choice)

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Question 70

Graph the function. - $y=-\cot (\pi x)$ $Graph the function. - y=-\cot (\pi x)$

(Multiple Choice)

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Question 71

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $g ( \theta ) = \sin \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

(Multiple Choice)

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Question 72

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

(Multiple Choice)

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Question 73

Graph the function. Show at least one period. - $y=-5 \sin \left(4 x+\frac{\pi}{2}\right)$ $Graph the function. Show at least one period. - y=-5 \sin \left(4 x+\frac{\pi}{2}\right)$

(Multiple Choice)

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Question 74

Without graphing the function, determine its amplitude or period as requested. - $y = - 3 \cos x \quad$ Find the period.

(Multiple Choice)

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Question 75

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 1,080 ^ { \circ }$

(Multiple Choice)

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Question 76

Graph the function. Show at least one period. - $y=5 \sin (\pi x+4)$ $Graph the function. Show at least one period. - y=5 \sin (\pi x+4)$

(Multiple Choice)

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Question 77

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

(Multiple Choice)

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Question 78

Find an equation for the graph. -

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Question 79

Write the equation of a sine function that has the given characteristics. -Amplitude: 2 Period: $\pi$ Phase Shift: $\frac { 7 } { 2 }$

(Multiple Choice)

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Question 80

Showing 61 - 80 of 354

Solve the problem. -A weight hangs from a rope 20 feet long. It swings through an angle of $27 ^ { \circ }$ each second. How far does the weight travel each second? Round to the nearest $0.1$ foot.

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

Graph the function. - $y=-\cot x$ $Graph the function. - y=-\cot x$

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=\sin x-2$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=\sin x-2$

Write the word or phrase that best completes each statement or answers the question. -Determine the sign of the trigonometric values listed below. (i) $\sin 250 ^ { \circ }$ (ii) $\tan 330 ^ { \circ }$ (iii) $\cos \left( - 40 ^ { \circ } \right)$

Graph the function. - $y=-\cot (2 x)$ $Graph the function. - y=-\cot (2 x)$

Solve the problem. -If $f ( \theta ) = \cos \theta$ and $f ( a ) = - \frac { 1 } { 12 }$ , find the exact value of $f ( a ) + f ( a - 2 \pi ) + f ( a + 4 \pi )$ .

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

Solve the problem. -What is the range of the tangent function?

Graph the function. - $y=-\cot (\pi x)$ $Graph the function. - y=-\cot (\pi x)$

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $g ( \theta ) = \sin \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

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

Graph the function. Show at least one period. - $y=-5 \sin \left(4 x+\frac{\pi}{2}\right)$ $Graph the function. Show at least one period. - y=-5 \sin \left(4 x+\frac{\pi}{2}\right)$

Without graphing the function, determine its amplitude or period as requested. - $y = - 3 \cos x \quad$ Find the period.

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 1,080 ^ { \circ }$

Graph the function. Show at least one period. - $y=5 \sin (\pi x+4)$ $Graph the function. Show at least one period. - y=5 \sin (\pi x+4)$

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

Find an equation for the graph. -

Write the equation of a sine function that has the given characteristics. -Amplitude: 2 Period: $\pi$ Phase Shift: $\frac { 7 } { 2 }$

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

Solve the problem. -A weight hangs from a rope 20 feet long. It swings through an angle of 27∘27 ^ { \circ }27∘ each second. How far does the weight travel each second? Round to the nearest 0.10.10.1 foot.

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

Graph the function. - y=−cot⁡xy=-\cot xy=−cotx

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=sin⁡x−2y=\sin x-2y=sinx−2

Graph the function. - y=−cot⁡(2x)y=-\cot (2 x)y=−cot(2x)

Solve the problem. -If f(θ)=cos⁡θf ( \theta ) = \cos \thetaf(θ)=cosθ and f(a)=−112f ( a ) = - \frac { 1 } { 12 }f(a)=−121​ , find the exact value of f(a)+f(a−2π)+f(a+4π)f ( a ) + f ( a - 2 \pi ) + f ( a + 4 \pi )f(a)+f(a−2π)+f(a+4π) .

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

Solve the problem. -What is the range of the tangent function?

Graph the function. - y=−cot⁡(πx)y=-\cot (\pi x)y=−cot(πx)

Find the exact value of the expression if θ = 60°. Do not use a calculator. - g(θ)=sin⁡θg ( \theta ) = \sin \theta \quadg(θ)=sinθ Find [g(θ)]2[ g ( \theta ) ] ^ { 2 }[g(θ)]2 .

Name the quadrant in which the angle θ lies. - sin⁡θ>0,cos⁡θ>0\sin \theta > 0 , \quad \cos \theta > 0sinθ>0,cosθ>0

Graph the function. Show at least one period. - y=−5sin⁡(4x+π2)y=-5 \sin \left(4 x+\frac{\pi}{2}\right)y=−5sin(4x+2π​)

Without graphing the function, determine its amplitude or period as requested. - y=−3cos⁡xy = - 3 \cos x \quady=−3cosx Find the period.

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - csc⁡1,080∘\csc 1,080 ^ { \circ }csc1,080∘

Graph the function. Show at least one period. - y=5sin⁡(πx+4)y=5 \sin (\pi x+4)y=5sin(πx+4)

Find the exact value. Do not use a calculator. - cos⁡(−π)\cos ( - \pi )cos(−π)

Find an equation for the graph. -

Write the equation of a sine function that has the given characteristics. -Amplitude: 2 Period: π\piπ Phase Shift: 72\frac { 7 } { 2 }27​

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

Solve the problem. -A weight hangs from a rope 20 feet long. It swings through an angle of $27 ^ { \circ }$ each second. How far does the weight travel each second? Round to the nearest $0.1$ foot.

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

Graph the function. - $y=-\cot x$ $Graph the function. - y=-\cot x$

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=\sin x-2$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=\sin x-2$

Graph the function. - $y=-\cot (2 x)$ $Graph the function. - y=-\cot (2 x)$

Solve the problem. -If $f ( \theta ) = \cos \theta$ and $f ( a ) = - \frac { 1 } { 12 }$ , find the exact value of $f ( a ) + f ( a - 2 \pi ) + f ( a + 4 \pi )$ .

Graph the function. - $y=-\cot (\pi x)$ $Graph the function. - y=-\cot (\pi x)$

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $g ( \theta ) = \sin \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

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

Graph the function. Show at least one period. - $y=-5 \sin \left(4 x+\frac{\pi}{2}\right)$ $Graph the function. Show at least one period. - y=-5 \sin \left(4 x+\frac{\pi}{2}\right)$

Without graphing the function, determine its amplitude or period as requested. - $y = - 3 \cos x \quad$ Find the period.

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 1,080 ^ { \circ }$

Graph the function. Show at least one period. - $y=5 \sin (\pi x+4)$ $Graph the function. Show at least one period. - y=5 \sin (\pi x+4)$

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

Write the equation of a sine function that has the given characteristics. -Amplitude: 2 Period: $\pi$ Phase Shift: $\frac { 7 } { 2 }$