Exam 5: Trigonometric Functions

Use transformations to graph the function. - $y = \cos \left( \frac { \pi } { 2 } x \right)$ $Use transformations to graph the function. - y = \cos \left( \frac { \pi } { 2 } x \right)$

(Multiple Choice)

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Question 81

Find the exact value of the indicated trigonometric function of θ. - $\sin \theta = - \frac { 4 } { 9 } , \quad \tan \theta > 0 \quad$ Find $\sec \theta$

(Multiple Choice)

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Question 82

Convert the angle in radians to degrees. - $\frac { 12 \pi } { 3 }$

(Multiple Choice)

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Question 83

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

(Short Answer)

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Question 84

Find the exact value of the indicated trigonometric function of θ. - $\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quad$ Find $\csc \theta$

(Multiple Choice)

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Question 85

Find an equation for the graph. -

(Multiple Choice)

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Question 86

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. - $\sin ( - \pi )$

(Multiple Choice)

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Question 87

Without graphing the function, determine its amplitude or period as requested. - $y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quad$ Find the period.

(Multiple Choice)

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Question 88

Write the word or phrase that best completes each statement or answers the question. -The following data represents the normal monthly precipitation for a certain city in California. Month, x Normal Monthly Precipitation, inches January, 1 6.06 February, 2 4.45 March, 3 4.38 April, 4 2.08 May, 5 1.27 June, 6 0.56 July, 7 0.17 August, 8 0.46 September, 9 0.91 October, 10 2.24 November, 11 5.21 December, 12 5.51 Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form y = A sin (ωx - Φ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram. $Write the word or phrase that best completes each statement or answers the question. -The following data represents the normal monthly precipitation for a certain city in California. \begin{array} { l | c } \text { Month, x } & \text { Normal Monthly } \\ \text { Precipitation, inches } \\ \hline \text { January, 1 } & 6.06 \\ \text { February, 2 } & 4.45 \\ \text { March, } 3 & 4.38 \\ \text { April, } 4 & 2.08 \\ \text { May, 5 } & 1.27 \\ \text { June, } 6 & 0.56 \\ \text { July, } 7 & 0.17 \\ \text { August, 8 } & 0.46 \\ \text { September, } 9 & 0.91 \\ \text { October, 10 } & 2.24 \\ \text { November, 11 } & 5.21 \\ \text { December, 12 } & 5.51 \end{array} Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form y = A sin (ωx - Φ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.$

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Question 89

Solve the problem. -For the equation $y = - \frac { 1 } { 2 } \sin ( 4 x + 3 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

(Multiple Choice)

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Question 90

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 660 ^ { \circ }$

(Multiple Choice)

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Question 91

Graph the function. Show at least one period. - $y=4 \sin (3 \pi x+3)$ $Graph the function. Show at least one period. - y=4 \sin (3 \pi x+3)$

(Multiple Choice)

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Question 92

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

(Multiple Choice)

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Question 93

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. - $\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta =$ ?

(Multiple Choice)

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Question 94

Solve the problem. -The Earth rotates about its pole once every 24 hours. The distance from the pole to a location on Earth 35° north latitude is about 3,243.8 miles. Therefore, a location on Earth at 35° north latitude is spinning on a circle of Radius 3,243.8 miles. Compute the linear speed on the surface of the Earth at 35° north latitude.

(Multiple Choice)

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Question 95

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $7 g ( \theta )$ .

(Multiple Choice)

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Question 96

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. - $\csc \left( - \frac { \pi } { 2 } \right)$

(Multiple Choice)

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Question 97

Solve the problem. -The data below represent the average monthly cost of natural gas in an Oregon home. Month Aug Sep Oct Nov Dec Jan Cost 21.20 28.24 44.73 67.25 89.77 106.26 Month Feb Mar Apr May Jun Jul Cost 111.30 106.26 89.77 67.25 43.73 28.24 $Solve the problem. -The data below represent the average monthly cost of natural gas in an Oregon home. \begin{array}{l} \begin{array} { l | c c c c c c } \text { Month } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Jan } \\ \hline \text { Cost } & 21.20 & 28.24 & 44.73 & 67.25 & 89.77 & 106.26 \end{array}\\\\ \begin{array} { l | c c c c c c } \text { Month } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } \\ \hline \text { Cost } & 111.30 & 106.26 & 89.77 & 67.25 & 43.73 & 28.24 \end{array} \end{array} Above is the graph of 45.05 \sin x superimposed over a scatter diagram of the data. Find the sinusoidal function o form y = A \sin ( \omega x - \varphi ) + B which best fits the data.$ Above is the graph of $45.05 \sin x$ superimposed over a scatter diagram of the data. Find the sinusoidal function o form $y = A \sin ( \omega x - \varphi ) + B$ which best fits the data.

(Multiple Choice)

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Question 98

Graph the function. Show at least one period. - $y=4 \sin (-2 x-\pi)$ $Graph the function. Show at least one period. - y=4 \sin (-2 x-\pi)$

(Multiple Choice)

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Question 99

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of $30 ^ { \circ }$ . Round to the nearest hundredth.

(Multiple Choice)

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Question 100

Showing 81 - 100 of 354

Use transformations to graph the function. - $y = \cos \left( \frac { \pi } { 2 } x \right)$ $Use transformations to graph the function. - y = \cos \left( \frac { \pi } { 2 } x \right)$

Find the exact value of the indicated trigonometric function of θ. - $\sin \theta = - \frac { 4 } { 9 } , \quad \tan \theta > 0 \quad$ Find $\sec \theta$

Convert the angle in radians to degrees. - $\frac { 12 \pi } { 3 }$

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

Find the exact value of the indicated trigonometric function of θ. - $\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quad$ Find $\csc \theta$

Find an equation for the graph. -

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. - $\sin ( - \pi )$

Without graphing the function, determine its amplitude or period as requested. - $y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quad$ Find the period.

Solve the problem. -For the equation $y = - \frac { 1 } { 2 } \sin ( 4 x + 3 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 660 ^ { \circ }$

Graph the function. Show at least one period. - $y=4 \sin (3 \pi x+3)$ $Graph the function. Show at least one period. - y=4 \sin (3 \pi x+3)$

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

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. - $\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta =$ ?

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $7 g ( \theta )$ .

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. - $\csc \left( - \frac { \pi } { 2 } \right)$

Graph the function. Show at least one period. - $y=4 \sin (-2 x-\pi)$ $Graph the function. Show at least one period. - y=4 \sin (-2 x-\pi)$

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of $30 ^ { \circ }$ . Round to the nearest hundredth.

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

Use transformations to graph the function. - y=cos⁡(π2x)y = \cos \left( \frac { \pi } { 2 } x \right)y=cos(2π​x)

Find the exact value of the indicated trigonometric function of θ. - sin⁡θ=−49,tan⁡θ>0\sin \theta = - \frac { 4 } { 9 } , \quad \tan \theta > 0 \quadsinθ=−94​,tanθ>0 Find sec⁡θ\sec \thetasecθ

Convert the angle in radians to degrees. - 12π3\frac { 12 \pi } { 3 }312π​

Find the exact value of the indicated trigonometric function of θ. - cot⁡θ=−98,cos⁡θ<0\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quadcotθ=−89​,cosθ<0 Find csc⁡θ\csc \thetacscθ

Find an equation for the graph. -

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. - sin⁡(−π)\sin ( - \pi )sin(−π)

Without graphing the function, determine its amplitude or period as requested. - y=76sin⁡(−8π3x)y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quady=67​sin(−38π​x) Find the period.

Solve the problem. -For the equation y=−12sin⁡(4x+3πy = - \frac { 1 } { 2 } \sin ( 4 x + 3 \piy=−21​sin(4x+3π ), identify (i) the amplitude, (ii) the phase shift, and (iii) 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⁡660∘\csc 660 ^ { \circ }csc660∘

Graph the function. Show at least one period. - y=4sin⁡(3πx+3)y=4 \sin (3 \pi x+3)y=4sin(3πx+3)

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=sin⁡(x+π)y=\sin (x+\pi)y=sin(x+π)

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=18\mathrm { r } = 18r=18 feet, A=84\mathrm { A } = 84A=84 square feet, θ=\theta =θ= ?

Find the exact value of the expression if θ = 60°. Do not use a calculator. - g(θ)=cos⁡θg ( \theta ) = \cos \theta \quadg(θ)=cosθ Find 7g(θ)7 g ( \theta )7g(θ) .

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⁡(−π2)\csc \left( - \frac { \pi } { 2 } \right)csc(−2π​)

Graph the function. Show at least one period. - y=4sin⁡(−2x−π)y=4 \sin (-2 x-\pi)y=4sin(−2x−π)

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of 30∘30 ^ { \circ }30∘ . Round to the nearest hundredth.

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

Use transformations to graph the function. - $y = \cos \left( \frac { \pi } { 2 } x \right)$ $Use transformations to graph the function. - y = \cos \left( \frac { \pi } { 2 } x \right)$

Find the exact value of the indicated trigonometric function of θ. - $\sin \theta = - \frac { 4 } { 9 } , \quad \tan \theta > 0 \quad$ Find $\sec \theta$

Convert the angle in radians to degrees. - $\frac { 12 \pi } { 3 }$

Find the exact value of the indicated trigonometric function of θ. - $\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quad$ Find $\csc \theta$

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. - $\sin ( - \pi )$

Without graphing the function, determine its amplitude or period as requested. - $y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quad$ Find the period.

Solve the problem. -For the equation $y = - \frac { 1 } { 2 } \sin ( 4 x + 3 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 660 ^ { \circ }$

Graph the function. Show at least one period. - $y=4 \sin (3 \pi x+3)$ $Graph the function. Show at least one period. - y=4 \sin (3 \pi x+3)$

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

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. - $\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta =$ ?

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $7 g ( \theta )$ .

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. - $\csc \left( - \frac { \pi } { 2 } \right)$

Graph the function. Show at least one period. - $y=4 \sin (-2 x-\pi)$ $Graph the function. Show at least one period. - y=4 \sin (-2 x-\pi)$

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of $30 ^ { \circ }$ . Round to the nearest hundredth.