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

Problem

y=−6*cos(x)

Solution

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

2. Determine the amplitude by taking the absolute value of the coefficient A=−6

|A|=|−6|=6

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

Period=(2*π)/1=2*π

4. Find the phase shift by identifying the value of C Since there is no horizontal shift added to or subtracted from x C=0

Phase Shift=0

Final Answer

Amplitude=6,Period=2*π,Phase Shift=0

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