Find Amplitude, Period, and Phase Shift y=2cos(theta)

Problem

y=2*cos(θ)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(θ−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|=|2|

|A|=2

3. Calculate the period using the formula (2*π)/|B| In this equation, B=1

Period=(2*π)/1

Period=2*π

4. Identify the phase shift C Since there is no horizontal displacement added or subtracted from θ inside the cosine function, C=0

Phase Shift=0

Final Answer

Amplitude=2,Period=2*π,Phase Shift=0

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