Find Amplitude, Period, and Phase Shift y=-3cos(-2x+pi/2)

Problem

y=−3*cos(−2*x+π/2)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D or y=A*cos(B*x−C)+D

2. Factor out the coefficient of x inside the cosine function to clearly see the phase shift.

y=−3*cos(−2*(x−π/4))

3. Determine the amplitude by taking the absolute value of the coefficient A

Amplitude=|−3|=3

4. Determine the period using the formula P=(2*π)/|B| where B=−2

P=(2*π)/|−2|=(2*π)/2=π

5. Determine the phase shift by identifying the value of C in the factored form x−C

Phase Shift=π/4

Final Answer

Amplitude=3,Period=π,Phase Shift=π/4

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