1. Graphing: Sine and Cosine
Section 4.4 – Day 1

2. Sine and Cosine
Graphing:
𝑦=𝑎 sin 𝑏𝜃
and
𝑦=𝑎 cos 𝑏𝜃

3. Amplitude Definition: The amplitude is 𝑎 .
The distance from the x-axis to the curve in a trigonometric graph.
“The height of the wave.”
The amplitude is 𝑎 .

4. Period 360° 𝑏 or 2𝜋 𝑏 Definition: The length of one cycle.
“How long it takes for the shape of the function to repeat.”
The period is:
360° 𝑏 or 2𝜋 𝑏

5. Examples: 𝑦=3 sin 4𝜃 𝑦=− cos 3𝜃 Amplitude = 3 =3
Period = 360° 4 =90° or Period = 2𝜋 4 = 𝜋 2
𝑦=− cos 3𝜃
Amplitude = −1 =1
Period = 360° 3 =120° or Period = 2𝜋 3 = 2𝜋 3

6. Examples: 𝑦=− 1 4 sin 1 3 𝜃 𝑦=6 cos 1 2 𝜃 Amplitude = − 1 4 = 1 4
Period = 360° = 360° 1 ∙ 3 1 =1080° or P = 2𝜋 = 2𝜋 1 ∙ 3 1 =6𝜋
𝑦=6 cos 1 2 𝜃
Amplitude = 6 =6
Period = 360° = 360° 1 ∙ 2 1 =720° or P = 2𝜋 = 2𝜋 1 ∙ 2 1 =4𝜋

7. Homework: Due 3/9 𝑦=3 cos 𝜃 𝑦=4 sin 2𝜃 𝑦=−2 sin 𝜃 𝑦=−4 cos 3 4 𝜃
Find the amplitude and period of the following functions:
𝑦=3 cos 𝜃
𝑦=4 sin 2𝜃
𝑦=−2 sin 𝜃
𝑦=−4 cos 3 4 𝜃
𝑦= 1 2 sin 𝜃
𝑦= 3 4 cos 1 2 𝜃
𝑦=− 2 3 cos 𝜃
𝑦=−2 sin 3𝜃