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

Problem

y=3*cos(4*x)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where A is the amplitude, B relates to 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|=|3|

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

P=(2*π)/4

4. Simplify the period fraction.

P=π/2

5. Identify the phase shift by looking for a horizontal displacement C inside the cosine argument. Since there is no value subtracted from x inside the function, C=0

Phase Shift=0

Final Answer

Amplitude=3,Period=π/2,Phase Shift=0

Want more problems? Check here!