Exam 5: Trigonometric Functions

Graph the function. - $y=-\sec (x)$ $Graph the function. - y=-\sec (x) A) B) C) D)$ A) $Graph the function. - y=-\sec (x) A) B) C) D)$ B) $Graph the function. - y=-\sec (x) A) B) C) D)$ C) $Graph the function. - y=-\sec (x) A) B) C) D)$ D) $Graph the function. - y=-\sec (x) A) B) C) D)$

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Question 1

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Find the exact value of the expression. Do not use a calculator. - $\csc 60 ^ { \circ } - \cos 45 ^ { \circ }$

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Question 2

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

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Question 3

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

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Question 4

Solve the problem. -An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of $\frac { 1 } { 3 }$ radian is swept out, what is the linear speed of the object? A) $\frac { 1 } { 6 }$ radians/sec B) $6 \mathrm {~cm} / \mathrm { sec }$ C) 6 radians/sec D) $\frac { 1 } { 6 } \mathrm {~cm} / \mathrm { sec }$

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Question 5

Graph the function. - $y=\sec (3x$ $Graph the function. - y=\sec (3x A) B) C) D)$ A) $Graph the function. - y=\sec (3x A) B) C) D)$ B) $Graph the function. - y=\sec (3x A) B) C) D)$ C) $Graph the function. - y=\sec (3x A) B) C) D)$ D) $Graph the function. - y=\sec (3x A) B) C) D)$

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Question 6

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

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Question 7

Solve the problem. -If $\sin \theta = 0.3$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

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Question 8

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. - $\sqrt { 7 }$

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Question 9

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 9 ^ { \circ }$

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Question 10

Solve the problem. -The current I, in amperes, flowing through an ac (alternating current) circuit at time t, in seconds, is $I = 30 \sin ( 50 \pi t )$ What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0. $Solve the problem. -The current I, in amperes, flowing through an ac (alternating current) circuit at time t, in seconds, is I = 30 \sin ( 50 \pi t ) What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0.$

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Question 11

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

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Question 12

Solve the problem. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\sec \theta$

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Question 13

Find the exact value of the expression. Do not use a calculator. - $\sin 330 ^ { \circ } \sin 270 ^ { \circ }$

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Question 14

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

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Question 15

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 37 ^ { \circ }$

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Question 16

Find an equation for the graph. -

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Question 17

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 18.90 24.24 44.58 68.25 91.92 109.26 Month Feb Mar Apr May Jun Jul Cost 113.60 106.26 91.92 68.25 42.58 24.24 $Solve the problem. -The data below represent the average monthly cost of natural gas in an Oregon home. \begin{array}{l} \begin{array} { l | c c c c c c } \text { Month } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Jan } \\ \hline \text { Cost } & 18.90 & 24.24 & 44.58 & 68.25 & 91.92 & 109.26 \end{array}\\\\ \begin{array} { l | c c c c c c } \text { Month } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } \\ \hline \text { Cost } & 113.60 & 106.26 & 91.92 & 68.25 & 42.58 & 24.24 \end{array} \end{array} Above is the graph of 47.35 \sin x ake a scatter diagram of the data. Find the sinusoidal function of the form y = A \sin ( \omega x - \varphi ) + B which fits the data.$ Above is the graph of $47.35 \sin x$ ake a scatter diagram of the data. Find the sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ which fits the data.

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Question 18

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

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Question 19

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

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Question 20

Showing 1 - 20 of 366

Graph the function. - $y=-\sec (x)$ $Graph the function. - y=-\sec (x) A) B) C) D)$ A) $Graph the function. - y=-\sec (x) A) B) C) D)$ B) $Graph the function. - y=-\sec (x) A) B) C) D)$ C) $Graph the function. - y=-\sec (x) A) B) C) D)$ D) $Graph the function. - y=-\sec (x) A) B) C) D)$

Find the exact value of the expression. Do not use a calculator. - $\csc 60 ^ { \circ } - \cos 45 ^ { \circ }$

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

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

Graph the function. - $y=\sec (3x$ $Graph the function. - y=\sec (3x A) B) C) D)$ A) $Graph the function. - y=\sec (3x A) B) C) D)$ B) $Graph the function. - y=\sec (3x A) B) C) D)$ C) $Graph the function. - y=\sec (3x A) B) C) D)$ D) $Graph the function. - y=\sec (3x A) B) C) D)$

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

Solve the problem. -If $\sin \theta = 0.3$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. - $\sqrt { 7 }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 9 ^ { \circ }$

Solve the problem. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\sec \theta$

Find the exact value of the expression. Do not use a calculator. - $\sin 330 ^ { \circ } \sin 270 ^ { \circ }$

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

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 37 ^ { \circ }$

Find an equation for the graph. -

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

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

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

Review

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Exam 5: Trigonometric Functions

Graph the function. - y=−sec⁡(x)y=-\sec (x)y=−sec(x) A) B) C) D)

Find the exact value of the expression. Do not use a calculator. - csc⁡60∘−cos⁡45∘\csc 60 ^ { \circ } - \cos 45 ^ { \circ }csc60∘−cos45∘

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) .

Name the quadrant in which the angle θ lies. - tan⁡θ<0,sin⁡θ<0\tan \theta < 0 , \quad \sin \theta < 0tanθ<0,sinθ<0

Graph the function. - y=sec⁡(3xy=\sec (3xy=sec(3x A) B) C) D)

Find the exact value of the expression if θ = 45°. Do not use a calculator. - g(θ)=cos⁡θg ( \theta ) = \cos \theta \quadg(θ)=cosθ Find [g(θ)]2[ g ( \theta ) ] ^ { 2 }[g(θ)]2 .

Solve the problem. -If sin⁡θ=0.3\sin \theta = 0.3sinθ=0.3 , find the value of sin⁡θ+sin⁡(θ+2π)+sin⁡(θ+4π)\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )sinθ+sin(θ+2π)+sin(θ+4π) .

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. - 7\sqrt { 7 }7​

Use a calculator to find the approximate value of the expression rounded to two decimal places. - cos⁡9∘\cos 9 ^ { \circ }cos9∘

Solve the problem. -The current I, in amperes, flowing through an ac (alternating current) circuit at time t, in seconds, is I=30sin⁡(50πt)I = 30 \sin ( 50 \pi t )I=30sin(50πt) What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0.

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​) A) B) C) D)

Solve the problem. - sin⁡θ=14,cos⁡θ=154\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quadsinθ=41​,cosθ=415​​ Find sec⁡θ\sec \thetasecθ

Find the exact value of the expression. Do not use a calculator. - sin⁡330∘sin⁡270∘\sin 330 ^ { \circ } \sin 270 ^ { \circ }sin330∘sin270∘

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

Use a calculator to find the approximate value of the expression rounded to two decimal places. - tan⁡37∘\tan 37 ^ { \circ }tan37∘

Find an equation for the graph. -

Without graphing the function, determine its amplitude or period as requested. - y=sin⁡3xy = \sin 3 x \quady=sin3x Find the period.

Name the quadrant in which the angle θ lies. - cos⁡θ<0,csc⁡θ<0\cos \theta < 0 , \quad \csc \theta < 0cosθ<0,cscθ<0

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

Review

Filters

Graph the function. - $y=-\sec (x)$ $Graph the function. - y=-\sec (x) A) B) C) D)$ A) $Graph the function. - y=-\sec (x) A) B) C) D)$ B) $Graph the function. - y=-\sec (x) A) B) C) D)$ C) $Graph the function. - y=-\sec (x) A) B) C) D)$ D) $Graph the function. - y=-\sec (x) A) B) C) D)$

Find the exact value of the expression. Do not use a calculator. - $\csc 60 ^ { \circ } - \cos 45 ^ { \circ }$

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

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

Graph the function. - $y=\sec (3x$ $Graph the function. - y=\sec (3x A) B) C) D)$ A) $Graph the function. - y=\sec (3x A) B) C) D)$ B) $Graph the function. - y=\sec (3x A) B) C) D)$ C) $Graph the function. - y=\sec (3x A) B) C) D)$ D) $Graph the function. - y=\sec (3x A) B) C) D)$

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

Solve the problem. -If $\sin \theta = 0.3$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. - $\sqrt { 7 }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 9 ^ { \circ }$

Solve the problem. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\sec \theta$

Find the exact value of the expression. Do not use a calculator. - $\sin 330 ^ { \circ } \sin 270 ^ { \circ }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 37 ^ { \circ }$

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

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