Find Amplitude, Period, and Phase Shift y=-1/5*cos(1/5x)

Problem

y=−1/5*cos(1/5*x)

Solution

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

2. Determine the amplitude by taking the absolute value of the coefficient A where A=−1/5

|A|=|−1/5|=1/5

3. Calculate the period using the formula P=(2*π)/|B| where B=1/5

P=(2*π)/(1/5)=10*π

4. Find the phase shift by identifying the horizontal displacement C Since there is no value subtracted from x inside the cosine function, C=0

Phase Shift=0

Final Answer

Amplitude=1/5,Period=10*π,Phase Shift=0

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