Aim: What is the transformation of trig functions? Do Now: HW: Handout Graph: y = 2 sin x and y = 2 sin x + 1, 0 ≤ x ≤ 2π on the same set of axes

y = 2 sin x y = 2 sin x + 1

y = 2 sin x + 1 is just shifted y = 2 sin x one unit up. They are both the transformations of the basic equation y = sin x Compare y = sin x and y = 2 sin 2x + 1 the amplitude changed from one to two the frequency changed from one to two the period changed from 2π to π the entire graph shift up one unit

Amplitude Frequency Vertical shift Notice that the sine and cosine functions have the same properties in terms of transformation.

Graph: y = 3 cos (2x) – 2, 0 ≤ x ≤ 2π

Given y = sin x Tell how each of the following equation transformed y = sin x 1. y = 2 sin x 2. y = 2 sin 4x 3. y = 2 sin 4x y = -2 sin 4x + 2

Given y = cos x Tell how each of the following equation transformed from y = cos x

Write the equation based on the graph

If the period of the equation y = – 2 sin Bx is, find the value of B If the period of the equation y = 3 cos Bx is 2, find the value of B.