Exam 4: Graphs of the Circular Functions

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 } \mathrm { sec }$ , what is the frequency of the system?

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Question 81

Graph the function. - $y = \csc \left( x - \frac { \pi } { 2 } \right)$ $Graph the function. - y = \csc \left( x - \frac { \pi } { 2 } \right)$

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Question 82

Use Identities to find the exact value. -A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 5 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

(Multiple Choice)

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Question 83

Match the function with its graph. -1) $y = 2 + \sin x$ 2) $y = 2 + \cos x$ 3) $y = - 2 + \sin x$ 4) $y = - 2 + \cos x$ a) $Match the function with its graph. -1) y = 2 + \sin x 2) y = 2 + \cos x 3) y = - 2 + \sin x 4) y = - 2 + \cos x a) b) c) d)$ b) $Match the function with its graph. -1) y = 2 + \sin x 2) y = 2 + \cos x 3) y = - 2 + \sin x 4) y = - 2 + \cos x a) b) c) d)$ c) $Match the function with its graph. -1) y = 2 + \sin x 2) y = 2 + \cos x 3) y = - 2 + \sin x 4) y = - 2 + \cos x a) b) c) d)$ d) $Match the function with its graph. -1) y = 2 + \sin x 2) y = 2 + \cos x 3) y = - 2 + \sin x 4) y = - 2 + \cos x a) b) c) d)$

(Multiple Choice)

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Question 84

Find the phase shift of the function. - $y = 5 - 3 \sin \left( 4 x + \frac { \pi } { 4 } \right)$

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Question 85

Graph the function. - $y = \frac { 1 } { 4 } \tan 2 x$ $Graph the function. - y = \frac { 1 } { 4 } \tan 2 x$

(Multiple Choice)

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Question 86

Give the amplitude or period as requested. -Period of $y = \cos \frac { 1 } { 3 } x$

(Multiple Choice)

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Question 87

Match the function with its graph. -1) $y = \sec x$ 2) $y = \csc x$ 3) $y = - \sec x$ 4) $y = - \csc x$ a) $Match the function with its graph. -1) y = \sec x 2) y = \csc x 3) y = - \sec x 4) y = - \csc x a) b) c) d)$ b) $Match the function with its graph. -1) y = \sec x 2) y = \csc x 3) y = - \sec x 4) y = - \csc x a) b) c) d)$ c) $Match the function with its graph. -1) y = \sec x 2) y = \csc x 3) y = - \sec x 4) y = - \csc x a) b) c) d)$ d) $Match the function with its graph. -1) y = \sec x 2) y = \csc x 3) y = - \sec x 4) y = - \csc x a) b) c) d)$

(Multiple Choice)

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Question 88

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph. -

(Multiple Choice)

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Question 89

Solve the problem. -Ignoring friction, the time, $t$ (in seconds), required for a block to slide down an inclined plane is given by the formula $t = \sqrt { \frac { 2 b } { g \sin \theta \cos \theta } }$ where $b$ is the length of the base in feet and $g = 32.2$ feet per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with a base of 12 feet at an angle of $36 ^ { \circ }$ ? Round your answer to three decimal places.

(Multiple Choice)

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Question 90

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

(Multiple Choice)

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Question 91

Solve the problem. -A generator produces an alternating current according to the equation I = 48 sin 109πt, where t is time in seconds and I is the current in amperes. What is the smallest time t such that I = 24?

(Multiple Choice)

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Question 92

Graph the function. - $y=\csc \left(\frac{3}{4} x-\frac{\pi}{4}\right)$ $Graph the function. - y=\csc \left(\frac{3}{4} x-\frac{\pi}{4}\right)$

(Multiple Choice)

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Question 93

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

(Multiple Choice)

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Question 94

Graph the function. - $y=\frac{1}{3} \csc \left(\frac{4}{5} x+\frac{\pi}{2}\right)$ $Graph the function. - y=\frac{1}{3} \csc \left(\frac{4}{5} x+\frac{\pi}{2}\right)$

(Multiple Choice)

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Question 95

Solve the problem. -Determine the length of a pendulum that has a period of 4 seconds.

(Multiple Choice)

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Question 96

Graph the function. - $y = \frac { 3 } { 2 } \cot x$ $Graph the function. - y = \frac { 3 } { 2 } \cot x$

(Multiple Choice)

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Question 97

Find the specified quantity. -Find the period of $y = - 5 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 3 } \right)$ .

(Multiple Choice)

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Question 98

Graph the function. - $y=\frac{3}{4} \cot \left(\frac{1}{3} x-\frac{\pi}{2}\right)$ $Graph the function. - y=\frac{3}{4} \cot \left(\frac{1}{3} x-\frac{\pi}{2}\right)$

(Multiple Choice)

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Question 99

Give the amplitude or period as requested. -Amplitude of $y = \sin 5 x$

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Question 100

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Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 } \mathrm { sec }$ , what is the frequency of the system?

Graph the function. - $y = \csc \left( x - \frac { \pi } { 2 } \right)$ $Graph the function. - y = \csc \left( x - \frac { \pi } { 2 } \right)$

Find the phase shift of the function. - $y = 5 - 3 \sin \left( 4 x + \frac { \pi } { 4 } \right)$

Graph the function. - $y = \frac { 1 } { 4 } \tan 2 x$ $Graph the function. - y = \frac { 1 } { 4 } \tan 2 x$

Give the amplitude or period as requested. -Period of $y = \cos \frac { 1 } { 3 } x$

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph. -

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Solve the problem. -A generator produces an alternating current according to the equation I = 48 sin 109πt, where t is time in seconds and I is the current in amperes. What is the smallest time t such that I = 24?

Graph the function. - $y=\csc \left(\frac{3}{4} x-\frac{\pi}{4}\right)$ $Graph the function. - y=\csc \left(\frac{3}{4} x-\frac{\pi}{4}\right)$

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

Graph the function. - $y=\frac{1}{3} \csc \left(\frac{4}{5} x+\frac{\pi}{2}\right)$ $Graph the function. - y=\frac{1}{3} \csc \left(\frac{4}{5} x+\frac{\pi}{2}\right)$

Solve the problem. -Determine the length of a pendulum that has a period of 4 seconds.

Graph the function. - $y = \frac { 3 } { 2 } \cot x$ $Graph the function. - y = \frac { 3 } { 2 } \cot x$

Find the specified quantity. -Find the period of $y = - 5 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 3 } \right)$ .

Graph the function. - $y=\frac{3}{4} \cot \left(\frac{1}{3} x-\frac{\pi}{2}\right)$ $Graph the function. - y=\frac{3}{4} \cot \left(\frac{1}{3} x-\frac{\pi}{2}\right)$

Give the amplitude or period as requested. -Amplitude of $y = \sin 5 x$

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

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Exam 4: Graphs of the Circular Functions

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is 13sec\frac { 1 } { 3 } \mathrm { sec }31​sec , what is the frequency of the system?

Graph the function. - y=csc⁡(x−π2)y = \csc \left( x - \frac { \pi } { 2 } \right)y=csc(x−2π​)

Match the function with its graph. -1) y=2+sin⁡xy = 2 + \sin xy=2+sinx 2) y=2+cos⁡xy = 2 + \cos xy=2+cosx 3) y=−2+sin⁡xy = - 2 + \sin xy=−2+sinx 4) y=−2+cos⁡xy = - 2 + \cos xy=−2+cosx a) b) c) d)

Find the phase shift of the function. - y=5−3sin⁡(4x+π4)y = 5 - 3 \sin \left( 4 x + \frac { \pi } { 4 } \right)y=5−3sin(4x+4π​)

Graph the function. - y=14tan⁡2xy = \frac { 1 } { 4 } \tan 2 xy=41​tan2x

Give the amplitude or period as requested. -Period of y=cos⁡13xy = \cos \frac { 1 } { 3 } xy=cos31​x

Match the function with its graph. -1) y=sec⁡xy = \sec xy=secx 2) y=csc⁡xy = \csc xy=cscx 3) y=−sec⁡xy = - \sec xy=−secx 4) y=−csc⁡xy = - \csc xy=−cscx a) b) c) d)

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph. -

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Solve the problem. -A generator produces an alternating current according to the equation I = 48 sin 109πt, where t is time in seconds and I is the current in amperes. What is the smallest time t such that I = 24?

Graph the function. - y=csc⁡(34x−π4)y=\csc \left(\frac{3}{4} x-\frac{\pi}{4}\right)y=csc(43​x−4π​)

Graph the function. - y=sec⁡(x−π4)y = \sec \left( x - \frac { \pi } { 4 } \right)y=sec(x−4π​)

Graph the function. - y=13csc⁡(45x+π2)y=\frac{1}{3} \csc \left(\frac{4}{5} x+\frac{\pi}{2}\right)y=31​csc(54​x+2π​)

Solve the problem. -Determine the length of a pendulum that has a period of 4 seconds.

Graph the function. - y=32cot⁡xy = \frac { 3 } { 2 } \cot xy=23​cotx

Find the specified quantity. -Find the period of y=−5cos⁡(14x+π3)y = - 5 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 3 } \right)y=−5cos(41​x+3π​) .

Graph the function. - y=34cot⁡(13x−π2)y=\frac{3}{4} \cot \left(\frac{1}{3} x-\frac{\pi}{2}\right)y=43​cot(31​x−2π​)

Give the amplitude or period as requested. -Amplitude of y=sin⁡5xy = \sin 5 xy=sin5x

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 } \mathrm { sec }$ , what is the frequency of the system?

Graph the function. - $y = \csc \left( x - \frac { \pi } { 2 } \right)$ $Graph the function. - y = \csc \left( x - \frac { \pi } { 2 } \right)$

Find the phase shift of the function. - $y = 5 - 3 \sin \left( 4 x + \frac { \pi } { 4 } \right)$

Graph the function. - $y = \frac { 1 } { 4 } \tan 2 x$ $Graph the function. - y = \frac { 1 } { 4 } \tan 2 x$

Give the amplitude or period as requested. -Period of $y = \cos \frac { 1 } { 3 } x$

Graph the function. - $y=\csc \left(\frac{3}{4} x-\frac{\pi}{4}\right)$ $Graph the function. - y=\csc \left(\frac{3}{4} x-\frac{\pi}{4}\right)$

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

Graph the function. - $y=\frac{1}{3} \csc \left(\frac{4}{5} x+\frac{\pi}{2}\right)$ $Graph the function. - y=\frac{1}{3} \csc \left(\frac{4}{5} x+\frac{\pi}{2}\right)$

Graph the function. - $y = \frac { 3 } { 2 } \cot x$ $Graph the function. - y = \frac { 3 } { 2 } \cot x$

Find the specified quantity. -Find the period of $y = - 5 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 3 } \right)$ .

Graph the function. - $y=\frac{3}{4} \cot \left(\frac{1}{3} x-\frac{\pi}{2}\right)$ $Graph the function. - y=\frac{3}{4} \cot \left(\frac{1}{3} x-\frac{\pi}{2}\right)$

Give the amplitude or period as requested. -Amplitude of $y = \sin 5 x$