Find Amplitude, Period, and Phase Shift y=-5cos(1/4x+pi/4)

Problem

y=−5*cos(1/4*x+π/4)

Solution

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

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

|A|=|−5|

|A|=5

3. Determine the period using the formula P=(2*π)/B where B=1/4

P=(2*π)/(1/4)

P=8*π

4. Determine the phase shift using the formula C/B First, rewrite the argument as 1/4*x−(−π/4) to identify C=−π/4

Phase Shift=(−π/4)/(1/4)

Phase Shift=−π

Final Answer

Amplitude=5,Period=8*π,Phase Shift=−π

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