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Aim: What is the transformation of trig functions?

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

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Aim: What is the transformation of trig functions?

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

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

  3. 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

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

  5. Graph: y = 3 cos (2x) – 2, 0 ≤ x ≤ 2π

  6. 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

  7. Given y = cos x Tell how each of the following equation transformed from y = cos x 1. 2. 3. 4.

  8. Write the equation based on the graph

  9. 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.

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