Find Amplitude, Period, and Phase Shift y=-3cos(1/4)x

Problem

y=−3*cos(1/4*x)

Solution

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

2. Determine the values of the constants from the given equation y=−3*cos(1/4*x) where A=−3 B=1/4 C=0 and D=0

3. Calculate the amplitude using the formula Amplitude=|A|

Amplitude=|−3|=3

4. Calculate the period using the formula Period=(2*π)/|B|

Period=(2*π)/(1/4)=8*π

5. Determine the phase shift using the value of C Since there is no horizontal shift inside the argument of the cosine function, the phase shift is 0

Phase Shift=0

Final Answer

Amplitude=3,Period=8*π,Phase Shift=0

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