Hi, I need help with these questions, they are easy, it’s just a matter of time

The sine and cosine curves y = a sin(kx)

and

y = a cos(kx), k > 0

have amplitude

and period

. The sine curve

y = 8 sin(2x)

has amplitude

and period

.

2.

–/1 pointsSPreCalc7 5.3.004.

My NotesAsk Your Teacher

The sine curve y = a sin(k(x − b))

has amplitude

, period

, and horizontal shift

. The sine curve

y = 9 sin

5

x −

π

4

has amplitude

, period

, and horizontal shift

.

3.

–/1 pointsSPreCalc7 5.3.010.

My NotesAsk Your Teacher

Graph the function.f(x) = −3 + cos(x)

4.

–/1 pointsSPreCalc7 5.3.014.

My NotesAsk Your Teacher

Graph the function.g(x) = −

5

8

cos(x)

5.

–/1 pointsSPreCalc7 5.3.015.

My NotesAsk Your Teacher

Graph the function.g(x) = 3 + 4 cos(x)

6.

–/1 pointsSPreCalc7 5.3.020.

My NotesAsk Your Teacher

Find the amplitude and period of the function.y = −sin(4x)

amplitude
period

Sketch the graph of the function.

7.

–/1 pointsSPreCalc7 5.3.022.

My NotesAsk Your Teacher

Find the amplitude and period of the function.y = cos(4πx)

amplitude
period

Sketch the graph of the function.

8.

–/1 pointsSPreCalc7 5.3.031.

My NotesAsk Your Teacher

Find the amplitude and period of the function.y = 3 +

1

3

cos(πx)

amplitude
period

Sketch the graph of the function.

9.

–/1 pointsSPreCalc7 5.3.037.

My NotesAsk Your Teacher

Find the amplitude, period, and phase shift of the function.y = −9 sin

5

x +

π

5

amplitude
period
phase shift

Graph one complete period.

10.

–/1 pointsSPreCalc7 5.3.042.

My NotesAsk Your Teacher

Find the amplitude, period, and phase shift of the function.y = 1 + cos

3x +

π

4

amplitude
period
phase shift

Graph one complete period.

11.

–/1 pointsSPreCalc7 5.3.045.

My NotesAsk Your Teacher

Find the amplitude, period, and phase shift of the function.y = sin(π + 2x)

amplitude
period
phase shift

Graph one complete period.

12.

–/1 pointsSPreCalc7 5.3.048.

My NotesAsk Your Teacher

The graph of one complete period of a cosine curve is given.

(a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.)

amplitude
period
horizontal shift

(b) Write an equation that represents the curve in the form

y = a cos(k(x − b)).

y =

13.

–/1 pointsSPreCalc7 5.3.050.MI.

My NotesAsk Your Teacher

The graph of one complete period of a sine curve is given.

(a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.)

amplitude
period
horizontal shift

(b) Write an equation that represents the curve in the form

y = a sin(k(x − b)).

y =

14.

–/1 pointsSPreCalc7 5.3.056.

My NotesAsk Your Teacher

A graphing calculator is recommended.

Determine an appropriate viewing rectangle for the function, and use it to draw the graph.f(x) = 7 sin(170x)

15.

–/1 pointsSPreCalc7 5.3.060.

My NotesAsk Your Teacher

A graphing calculator is recommended.

Determine an appropriate viewing rectangle for the function, and use it to draw the graph.f(x) = csc(40x)

16.

–/1 pointsSPreCalc7 5.3.067.

My NotesAsk Your Teacher

A graphing calculator is recommended.

Graph the three functions on a common screen.y = x², y = −x², y = x² sin(x)

How are the graphs related?

y = x² sin(x)

is a sine curve that oscillates about the graph of

y = x².

y = x² sin(x)

is a fourth degree polynomial that lies between the graphs of

y = x²

and

y = −x².

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