Find Amplitude, Period, and Phase Shift y=1/2*cos(8x)

Problem

y=1/2*cos(8*x)

Solution

1. Identify the standard form of the cosine function, which is y=A*cos(B*(x−C))+D where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

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

|A|=|1/2|=1/2

3. Calculate the period using the formula Period=(2*π)/|B| In this equation, B=8

Period=(2*π)/8

Period=π/4

4. Find the phase shift by identifying the value of C Since there is no horizontal translation inside the cosine function (8*x is the same as 8(x - 0)),t*h*e*p*h*a*s(e)*s(h)*i*ƒ*t*i*s()$.

Phase Shift=0

Final Answer

Amplitude=1/2,Period=π/4,Phase Shift=0

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