HPC Section 4.5 Graphing Trig Functions Part 1

PC Section 4.5 Graphing Trig Functions

Part 1
Graphs of sine and cosine.

But First, A video

Discovery Education

Graphing:

y = sin x

Graphing:

y = cos x

One period of the graph is highlighted in bold.

Graphing:

y = cos x - red

y = sin x - blue



So what happens when we incorporate a, b, c, and d?
For Example: y = a sin [b(x + c)] +d

I think you already know 3 out of 4.

Multiple Choice

Here is the parent function y = sin x. Which of the graphs below would represent y = 2 sin x?

Multiple Choice

Here is the parent function y = sin x. Which of the graphs below would represent y = sin x + 2?

Multiple Choice

Here is the parent function y = sin x. Which of the graphs below would represent y = sin (x + 2)?

Multiple Choice

Here is the parent function y = sin x. Which of the graphs below would represent y = sin 2x?

Multiple Choice

So describe what is happening to this graph?

y = 3 cos x

• Shifts up 3 spaces

• Shifts right 3 spaces

• Vertically stretches by a factor of 3

• Vertically Shrinks by a factor of 3

Multiple Choice

So describe what is happening to this graph?

y = 1/2 cos x + 1

• A vertical stretch and horizontal shift right 1 unit

• A vertical shrink and shift down 1 unit

• A vertical shrink and shift up 1 unit

• A vertical shift up 1/2 space and horizontal shift left 1

Open Ended

So describe what is happening to this graph?

y = - 4 sin (x - 3)

(can you name all three?)

Multiple Choice

$$y_1=\ \cos\ x\ -\pi$$  

$$y_2=\cos\ \left(x-\pi\right)$$
What is the difference between the two graphs?

• They are the same

• One graph shifts down by pi units and the other shifts right by pi units.

• One graph shifts up by pi units and one shifts down by pi units

• One graph shifts down by pi units and one shifts left by pi units

Sine and Cosine Parent functions

Let's review the basics

Graphing the Key Points:

 

Open Ended

How will the graph of y = 2 sin x differ from the parent function y = sin x?

y = sin x - Red
y = 2 sin x - Blue

This is called Amplitude - replaces our vertical stretch/shrink.

Open Ended

How will the graph of y = -4 cos x differ from the parent function y = cos x?

Homework

• Page 2

• #1, 2, 5, 7, 9, 10, 17, 25, 33, 35