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

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y

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y = 2 sin x

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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

DBxAy sin

AmplitudeFrequency

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 ≤ 2πMath Composer 1. 1. 5http: / / www. mathcomposer. com

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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 + 2

4. y = -2 sin 4x + 2

Given y = cos x

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

xy2

1cos32.

1. xy2

1cos

3. 12

1cos3 xy

4. 12

1cos3 xy

Write the equation based on the graph

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If the period of the equation y = – 2 sin Bx is

2

, find the value of B

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