Find Amplitude, Period, and Phase Shift y=-4cos(x)

Problem

y=−4*cos(x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=−4 The amplitude is the absolute value |A|

|A|=|−4|=4

3. Determine the value of B to find the period. In this equation, B=1 The formula for the period of a cosine function is (2*π)/B

Period=(2*π)/1=2*π

4. Determine the value of C to find the phase shift. Since there is no horizontal shift added or subtracted from x C=0

Phase Shift=0

Final Answer

Amplitude=4,Period=2*π,Phase Shift=0

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