Homework Midterm Unit Test 2

Determine the period of the function y=3sin(2x)

d. Pi

Determine the amplitude or period as requested.
Amplitude of 1/3cos2x

d. 1/3

Determine the amplitude or period as requested.
Amplitude of y=cos3x

b. 1

Determine the amplitude or period as requested.

Amplitude of y=3-4sin3x

A. 4

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Determine the amplitude or period as requested.

Amplitude of y=4sin 1/3x

A. 4

Determine the amplitude or period as requested.

Amplitude of y=-4cos1/3x

D. 4

Determine the amplitude or period as requested.

Amplitude of y=4cosx

B. 4

Determine the amplitude or period as requested.

Amplitude of y=sin5x

D. 1

Determine the amplitude or period as requested.

Amplitude of y=-3cos1/4x

D. 3

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Determine the period of the function y=-2sin(pi/2)x

D. 4

Determine the amplitude of the function y = 2 cos x from the graph shown below:

b.
2

The b in both of the graph types: affects the period (or wavelength) of the graph. What happens to the period as the value of b gets larger?

c.
period decreases

Determine the amplitude or period as requested.

Amplitude of y=sin3x

D. 1

Determine the amplitude or period as requested.

Period of y=4sin1/3x

D. 6pi

In the expression y=asin(x), what does the a stand for?

b.
amplitude

Determine the amplitude of the function y=-1/2cosx

C. 1/2

Determine the amplitude or period as requested.

Amplitude of y=5cosx

B. 5

Determine the amplitude or period as requested.

Amplitude of y=-5sinx

c. 5

Determine the amplitude or period as requested.

Amplitude of y=-2sinx

c. 2

Determine the amplitude or period as requested.

Amplitude of y=-1/5sinx

b. 1/5

Determine the amplitude or period as requested.

Amplitude of y= -2sinx

c. 2

In the expression y=asin(x), what does the a stand for?

b.
amplitude

Determine the amplitude or period as requested.

Period of y=-1/3sin2x

d. pi.

Determine the amplitude of the function y = 2 cos x from the graph shown below:

b. 2

Determine the period of the function y = -3cos(pi/2)x

d.
10

Determine the amplitude or period as requested.

Amplitude of y=-1/5sinx

b. 1/5

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The b in both of the graph types: affects the period (or wavelength) of the graph. What happens to the period as the value of b gets larger?

c.
period decreases

Determine the amplitude or period as requested.

Period of y=-2sinx

a. 2pi.

Determine the amplitude or period as requested.

Amplitude of y=3cos1/2x

b. 3

Determine the amplitude or period as requested.

Period of y=4sin1/3x

d. 6pi

Write the equation for the sine function shown below.

a.y=-sin5theta

A particular sound wave can be graphed using the function y=-10sin4x. Find the amplitude and period of the function.

A.

A particular sound wave can be graphed using the function y=-3sinx. Find the amplitude and period of the function

A.

Find the period of the graph shown below.

B. 2/3pi

Sketch one cycle of y = sin 2theta

C.

Use the graph to find the value of y = sin theta for the value of theta

240º

A. -0.9

Sketch one cycle of y = 4 sin 4theta

C.

Find the amplitude of the sine curve shown below.

c.
4

Find the amplitude of the sine curve shown below.

a.
2

Use the graph to find the value of y = sin theta for the value of theta

1/4 pi radians

b. 0.7

A particular sound wave can be graphed using the function y=1sin4x Find the amplitude and period of the function.

a.

Use the graph to find the value of y = sin theta for the value of theta
1/3 pi radians

c.
0.9

Write the equation for the sine function shown below.

c. y=5sin2theta

Find the period of the graph shown below.

a. 4pi.

Use the graph to find the value of y = sin theta for the value of theta.

270º

d.
-1

Use the graph to find the value of y = sin theta for the value of theta

360º

b.
0

Find the period of the graph shown below.

A. pi

Use the graph to find the value of y = sin theta for the value of theta.

330º

a.
-0.5

Find the period of the graph shown below.

A. 1/2pi.

Sketch one cycle of y = 2 sin theta

C.

Use the graph to find the value of y = sin theta for the value of theta.

90º

d.
1

Find the period, range, and amplitude of the cosine function
y=3/2 cos t/2

A.

Write a cosine function for the graph.

D. y=-2cos3theta

Suppose 8-in waves pass every 3 s. Write an equation that models the height of a water molecule as it moves from crest to crest.

D. 4cos 2pi/3 theta

Use a graphing calculator to solve the equation -6cos pi/3 theta=4 in the interval from 0 to 2pi. Round to the nearest hundredth.

b.
2.20, 3.80

cos(theta + 2pi) = cos theta

True

Write a cosine function for the graph.

C. -5cos theta

Write a cosine function for the graph.

B. y=3cos 3 theta

Write a cosine function for the graph.

C. 2cos4 theta

Write an equation of the cosine function with amplitude pi/2 and period 3.

A.

How does A compare to B?
A. Sin pi/2
B. cos(-pi)

A. A>=B

How does A compare to B?
A. Cos pi
B. Sin 3pi/2

c.
A = B

Write an equation of the cosine function with amplitude 2 and period 4pi.

C. y=2cos(1/2x)

Write a cosine function for the graph.

a. y=4cos2 theta

How does A compare to B?
A. sin pi/2
B. cos 0

c.
A = B

cos theta= cos (-theta)

true

How does A compare to B?
A. cos(theta+2pi)
B. cos(-theta)

c.
A = B

Write the equation for the inverse of the function.
y= Arctan(x+pi/2)

b. y=tanx=pi/2

Find the value of Tan^-1 squareroot 3/ 3

a. pi/6

Write the equation for the inverse of the function.

y = sin x

b.
y = Arcsin x

What is the value of Arc tan 1?

c. pi/4

Find the value of Arc cos 0

D. pi/2

Find the value of Sin^-1 0

B. 0

cos^1 (x) = -Cos^-1 x for -1<= x <= 1

False

Graph y= sin^-1 (-1/2x) the interval -5<= x <= 5

C.

Graph y=sin^-1 (1/4x) on the interval -5<= x <= 5

D.

Evaulate sin(Arccos(-9/square root 145))

A. 8/ squareroot 145

What is the value of cos(Tan^-1 1)?

D. square root 2 /2

Sin(Sin^-1x) = x for -1<= x <= 1

True

Find the value of tan(sin^-1(1/2))

c. square root 3/ 3

Write the equation for the inverse of the function.
y= pi/4 + sinx

c. y= Arcsin(x – pi/4)

Which describes the behavior of the function f(x)= tan^-1(x)

C.

Find the value of Sin^-1(tan pi/4)

d. Pi/2

Write the equation for the inverse of the function.

y = cos 2x

D.

Which function has a range of (-pi/2,pi/2)?

B. y= Tan ^-1 x.

Solve 2 cos theta + 2 = 3 in the interval from 0 to 2 theta Round to the nearest hundredth.

c.
1.05, 5.24

Write a cosine function for the graph.

y= -4 cos 4 theta

Find the amplitude and period of y = -5 sin (5x).

b.
amplitude = 5, period = 2/5 pi

Graph the following fnction on the interval -5 <= x <= 5
y= Arc cos (1/3x)

D.

Sketch one cycle of y = sin 2 theta

C.