Exam 4: Graphs of the Circular Functions

Graph the function over a one-period interval. - $y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)$

(Multiple Choice)

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Question 41

Solve the problem. -The weekly sales in thousands of items of a product has a seasonal sales record approximated by $\mathrm { n } = 62.39 + 22.4 \sin \frac { \pi \mathrm { t } } { 24 }$ ( $\mathrm { t } =$ time in weeks with $\mathrm { t } = 1$ referring to the first week in the year). During which week(s) will the sales equal 73,590 items?

(Multiple Choice)

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Question 42

Find the specified quantity. -Find the amplitude of $y = - 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)$ .

(Multiple Choice)

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Question 43

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

(Multiple Choice)

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Question 44

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

(Multiple Choice)

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Question 45

Graph the function over a one-period interval. - $y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$

(Multiple Choice)

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Question 46

Find the specified quantity. -Find the period of $y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)$ .

(Multiple Choice)

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Question 47

Solve the problem. -Suppose that a weight on a spring has an initial position of $s ( 0 ) = - 5$ inches and a period of $P = 2.5$ seconds. Find a function $s ( t ) = a \cos ( 2 \pi F t )$ that models the displacement of the weight.

(Multiple Choice)

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Question 48

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 2 \cos ( 6 \pi t )$ inches after $t$ seconds. What is the maximum height that the weight rises above the equilibrium position?

(Multiple Choice)

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Question 49

Give the amplitude or period as requested. -Amplitude of $y = - 3 \sin x$

(Multiple Choice)

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Question 50

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

(Multiple Choice)

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Question 51

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

(Multiple Choice)

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Question 52

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

(Multiple Choice)

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Question 53

Graph the function over a one-period interval. - $y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$ $Graph the function over a one-period interval. - y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$

(Multiple Choice)

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Question 54

Solve the problem. -A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

(Multiple Choice)

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Question 55

Graph the function over a one-period interval. - $y = \frac { 1 } { 2 } \sin ( x + \pi )$ $Graph the function over a one-period interval. - y = \frac { 1 } { 2 } \sin ( x + \pi )$

(Multiple Choice)

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Question 56

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

(Multiple Choice)

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Question 57

Find the phase shift of the function. - $y = 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)$

(Multiple Choice)

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Question 58

Graph the function over a one-period interval. - $y=3+\frac{1}{3} \sin (2 x-\pi)$ $Graph the function over a one-period interval. - y=3+\frac{1}{3} \sin (2 x-\pi)$

(Multiple Choice)

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Question 59

Graph the function over a one-period interval. - $y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)$

(Multiple Choice)

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Question 60

Showing 41 - 60 of 137

Graph the function over a one-period interval. - $y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)$

Find the specified quantity. -Find the amplitude of $y = - 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)$ .

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

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

Graph the function over a one-period interval. - $y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$

Find the specified quantity. -Find the period of $y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)$ .

Solve the problem. -Suppose that a weight on a spring has an initial position of $s ( 0 ) = - 5$ inches and a period of $P = 2.5$ seconds. Find a function $s ( t ) = a \cos ( 2 \pi F t )$ that models the displacement of the weight.

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 2 \cos ( 6 \pi t )$ inches after $t$ seconds. What is the maximum height that the weight rises above the equilibrium position?

Give the amplitude or period as requested. -Amplitude of $y = - 3 \sin x$

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

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

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

Graph the function over a one-period interval. - $y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$ $Graph the function over a one-period interval. - y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$

Solve the problem. -A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Graph the function over a one-period interval. - $y = \frac { 1 } { 2 } \sin ( x + \pi )$ $Graph the function over a one-period interval. - y = \frac { 1 } { 2 } \sin ( x + \pi )$

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

Find the phase shift of the function. - $y = 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)$

Graph the function over a one-period interval. - $y=3+\frac{1}{3} \sin (2 x-\pi)$ $Graph the function over a one-period interval. - y=3+\frac{1}{3} \sin (2 x-\pi)$

Graph the function over a one-period interval. - $y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)$

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

Graph the function over a one-period interval. - y=14cos⁡2(x+π4)y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)y=41​cos2(x+4π​)

Find the specified quantity. -Find the amplitude of y=−2sin⁡(4x+π2)y = - 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)y=−2sin(4x+2π​) .

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

Graph the function. - y=43sec⁡(12x+π4)y=\frac{4}{3} \sec \left(\frac{1}{2} x+\frac{\pi}{4}\right)y=34​sec(21​x+4π​)

Graph the function over a one-period interval. - y=12cos⁡4(x−π3)y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)y=21​cos4(x−3π​)

Find the specified quantity. -Find the period of y=−5sin⁡(8x+π2)y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)y=−5sin(8x+2π​) .

Solve the problem. -Suppose that a weight on a spring has an initial position of s(0)=−5s ( 0 ) = - 5s(0)=−5 inches and a period of P=2.5P = 2.5P=2.5 seconds. Find a function s(t)=acos⁡(2πFt)s ( t ) = a \cos ( 2 \pi F t )s(t)=acos(2πFt) that models the displacement of the weight.

Solve the problem. -The position of a weight attached to a spring is s(t)=−2cos⁡(6πt)s ( t ) = - 2 \cos ( 6 \pi t )s(t)=−2cos(6πt) inches after ttt seconds. What is the maximum height that the weight rises above the equilibrium position?

Give the amplitude or period as requested. -Amplitude of y=−3sin⁡xy = - 3 \sin xy=−3sinx

Graph the function. - y=3csc⁡(53x−π3)y=3 \csc \left(\frac{5}{3} x-\frac{\pi}{3}\right)y=3csc(35​x−3π​)

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

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

Graph the function over a one-period interval. - y=3cos⁡(x+π2)y = 3 \cos \left( x + \frac { \pi } { 2 } \right)y=3cos(x+2π​)

Solve the problem. -A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the period of the system is 13\frac { 1 } { 3 }31​ second, determine a trigonometric model that gives the position of the weight at time ttt seconds.

Graph the function over a one-period interval. - y=12sin⁡(x+π)y = \frac { 1 } { 2 } \sin ( x + \pi )y=21​sin(x+π)

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

Find the phase shift of the function. - y=3cos⁡(14x+π4)y = 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)y=3cos(41​x+4π​)

Graph the function over a one-period interval. - y=3+13sin⁡(2x−π)y=3+\frac{1}{3} \sin (2 x-\pi)y=3+31​sin(2x−π)

Graph the function over a one-period interval. - y=12+cos⁡(2x−2π3)y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)y=21​+cos(2x−32π​)

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

Graph the function over a one-period interval. - $y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)$

Find the specified quantity. -Find the amplitude of $y = - 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)$ .

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

Graph the function over a one-period interval. - $y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$

Find the specified quantity. -Find the period of $y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)$ .

Solve the problem. -Suppose that a weight on a spring has an initial position of $s ( 0 ) = - 5$ inches and a period of $P = 2.5$ seconds. Find a function $s ( t ) = a \cos ( 2 \pi F t )$ that models the displacement of the weight.

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 2 \cos ( 6 \pi t )$ inches after $t$ seconds. What is the maximum height that the weight rises above the equilibrium position?

Give the amplitude or period as requested. -Amplitude of $y = - 3 \sin x$

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

Graph the function over a one-period interval. - $y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$ $Graph the function over a one-period interval. - y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$

Solve the problem. -A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Graph the function over a one-period interval. - $y = \frac { 1 } { 2 } \sin ( x + \pi )$ $Graph the function over a one-period interval. - y = \frac { 1 } { 2 } \sin ( x + \pi )$

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

Find the phase shift of the function. - $y = 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)$

Graph the function over a one-period interval. - $y=3+\frac{1}{3} \sin (2 x-\pi)$ $Graph the function over a one-period interval. - y=3+\frac{1}{3} \sin (2 x-\pi)$

Graph the function over a one-period interval. - $y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)$