Find Amplitude, Period, and Phase Shift y=-5/9cos(7/3x)

Problem

y=−5/9*cos(7/3*x)

Solution

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

2. Determine the values of the constants from the given equation: A=−5/9 B=7/3 C=0 and D=0

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

Amplitude=|−5/9|=5/9

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

Period=(2*π)/7/3=(6*π)/7

5. Calculate the phase shift using the formula Phase Shift=C/B

Phase Shift=0/7/3=0

Final Answer

Amplitude=5/9,Period=(6*π)/7,Phase Shift=0

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