Graphing: Sine and Cosine Section 4.4 – Day 1

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

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 .

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

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

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

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