Find Amplitude, Period, and Phase Shift y=6cos(pix)

Problem

y=6*cos(π*x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=6 The amplitude is |A|

3. Determine the value of B to find the period. Here, B=π

4. Apply the formula for the period, which is P=(2*π)/|B|

5. Calculate the period by substituting B=π into the formula: P=(2*π)/π=2

6. Identify the phase shift C Since there is no horizontal shift inside the cosine function, C=0

Final Answer

Amplitude=6,Period=2,Phase Shift=0

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