Graphing Sine and Cosine

Amplitude Horizontal & Vertical Shifts

Period Length

Graphing Sine and Cosine

Complete this worksheet by using the following slides.

Graphing sine Graphing cosine

Graphing Sine

Radians Sin( )

0

2

32

2

?

?

?

?

?

To graph the sine function we need to plot points we already know from our unit circle. Find the x and y coordinates of the following values. The x values represent the radians and the y values represent the sine values. Click each ? button to see if your answer is correct.

Parent Graph of Sine

We need to plot the first point (0,0). Click to graph.

Next we need to graph the pointClick to graph.

,12

Plot and connect the rest of your points to create the parent function for Sine.

Click here to graph Cosine

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Graphing Cosine

Radians Cos( )

0

2

32

2

To graph the cosine function we need to plot points we already know from our unit circle. Find the x and y coordinates of the following values. The x values represent the radians and the y values represent the sine values. Click each ? button to see if your answer is correct.

?

?

?

?

?

Parent Graph of Cosine

We need to plot the first point (0,1). Click to graph.

Next we need to graph the pointClick to graph.

,02

Plot and connect the rest of your points to create the parent function for Cosine.

Click here to graph

Sine

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Amplitude

In this section complete this worksheet.

First use the general information to help you.

Next, use the video to help you understand how to graph.

Amplitude general information

In standard form , the a represents the amplitude. Amplitude is the distance from the midpoint to

the highest or lowest point on the graph. Steps to graph an amplitude change:1. Graph the parent function.2. Multiply each y coordinate by the

amplitude. 3. Plot each new point with the original x value

and new y value.

sin ( )y a b x c d

Graphing a change in amplitudeWatch and take notes on this video. Then try the two practice problems on your worksheet.

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Period Length

In this section complete this worksheet.

First use the general information to help you.

Next, use the video to help you understand how to graph.

Period length general information

In standard form , the b represents the period length. Period length is the distance between any two

repeating points on the graph. Steps to graph a period length change:1. Graph the parent function.2. Multiply each x coordinate by the reciprocal

of the b value. 3. Plot each new point with the original y value

and new x value.

cos ( )y a b x c d

Graphing a change in period length

Watch and take notes on this video. Then try the two practice problems on your worksheet.

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Horizontal Shift

In this section complete this worksheet.

First use the general information to help you.

Next, use the video to help you understand how to graph.

Horizontal shift general information

In standard form , the c represents the horizontal shift. Horizontal shift is the distance moved left or

right from the original function. Steps to graph a horizontal shift:1. Graph the parent function.2. Move each x value left (subtract) or right

(add) by the value of c. 3. Plot each new point and connect the lines.

cos ( )y a b x c d

Graphing a horizontal shiftWatch and take notes on this video. Then try the two practice problems on your worksheet.

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Vertical Shift

In this section complete this worksheet.

First use the general information to help you.

Next, use the video to help you understand how to graph.

Vertical shift general information

In standard form , the d represents the vertical shift. Vertical shift is the distance moved up or down

from the original function. Steps to graph a vertical shift:1. Graph the parent function.2. Move each y value up(+) or down(-) by the

value of d. 3. Plot each new point and connect the lines.

sin ( )y a b x c d

Graphing a vertical shiftWatch and take notes on this video. Then try the two practice problems on your worksheet.

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