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Date: _______________________
Chapter 11: Trig Graphs
Topic 5: PHASE SHIFT
Period: __________
Phase shift is the measure horizontal shifting. If the phase shift is positive then the horizontal shift is to the
right. If the phase shift is negative, then the horizontal shift is to the left.
When determining the direction of the phase shift, it is important to have the function in the proper form:
In general:
y = asin(bx – c) + d
y = acos(bx - c) + d
|A| = amplitude
B = frequency (cycles between 0 and 2π)
C = horizontal shift
- (x + c) shifts the graph left C units
- (x – c) shifts the graph right C units
D = vertical shift
When the value of D is positive, then the trigonometric graph shifts UP.
When the value of D is negative, then the trigonometric graph shifts DOWN.
Practice: Consider the function 𝑦 = sin 𝑥. Explain the shift of each graph below (include direction and
number of units)
𝜋
1. 𝑦 = sin(𝑥 + 90)
2. 𝑦 = sin𝑥 – 6
3. 𝑦 = sin (𝑥 − )
4
4. 𝑦 = 2sin(𝑥 – 180) + 3
𝜋
2
5. 𝑦 = sin (𝜃 + ) − 1