Lesson 4.5Graph of Sine & Cosine

Find your work on graphs of sine and cosine from the last couple of days.

Sine/Cosine Graph – Key Points

Properties of Sine & Cosine

Domain:

Range:

Intercepts:

(when y = 0)

Amplitude:

Period:

y = cos x

y = sin x

General Equation

y = a sin (bx – c) + d y = a cos (bx – c) + d

a → affects amplitude

b → affects period

c → shifts horizontally

d → shifts vertically

Endpoints of One-Cycle

Solve the equations:

bx – c = 0 and bx – c = 2л

Example 1: Discuss the graph of

3sin2

1 xy

Example 2: Write an equation for the graph below: