Find Amplitude, Period, and Phase Shift y=3cos(x+pi/4)

Problem

y=3*cos(x+π/4)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=3

3. Calculate the amplitude using the formula Amplitude=|A|

4. Determine the value of B to find the period. Here, B=1

5. Calculate the period using the formula Period=(2*π)/|B|

6. Determine the value of C to find the phase shift. Since the expression is x+π/4 we rewrite it as x−(−π/4) so C=−π/4

Final Answer

Amplitude=3

Period=2*π

Phase Shift=−π/4

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