Today you will use shifts and vertical stretches to graph and find the equations of sinusoidal functions. You will also learn the 5-point method for sketching

graphs.

4.1.4: How Do I Shift Trig Functions?

4.1.3 Homework

4.1.3 Homework

Today

What does the “normal” sine graph look like?

Recall from Lesson 4.1.3

Recall from Lesson 4.1.3What does the “normal” cosine graph look like?

Generating the Sine & Cosine Graph

Sine Wave Tracer

Draw the “normal” graph for each. Label the 5 key points.

Maximum? Minimum? Crossings?Period? Amplitude?Parent EquationGeneral Equation

Add Sine & Cosine to your Parent Graph Tool Kit Notes

Sine GraphPeriod: 2π

Amplitude: 1

Maximum:

Minimum:

Crossings:

( ,1)2

3( , 1)2

(0,0) ( ,0) (2 ,0)

Parent Equation: sinGeneral Equation: sin( ( ))

y xy a b x c d

Cosine GraphParent Equation: cosGeneral Equation: cos( ( ))

y xy a b x c d

Period: 2π

Amplitude: 1

Maximum:

Minimum:

Crossings:

(0,1) and (2 ,1)

( , 1) 3( ,0) ( ,0)

2 2

Transformations Review

siny A B x C D

Vertical Stretch/ Shrink

Horizontal Stretch/ Shrink

Left/ Right

Up/Down

Reflect over x-axis

Together as a Class

Amplitude and Period Changes

Complete4-49 & 4-50 with

your partner.

Partner Work

4-49 & 4-50

4-51 Class Discussion

5-point Method

5-52: Part a together as a class

4-52 a

Complete4-52 parts b, c, and d with your partner.

Partner Work

5-52: Practice

4-52 b

4-52 c

4-52 d

Use the 5-point method to help you sketch the graph for the function that was given to you.

Exit Slip

HW 4.1.44-53 to 4-61

(pg. 197)

Assignment