Find Amplitude, Period, and Phase Shift f(x)=5sin(x)+4sin(x)

Problem

ƒ(x)=5*sin(x)+4*sin(x)

Solution

1. Combine like terms to simplify the function into a single trigonometric expression.

ƒ(x)=9*sin(x)

2. Identify the standard form of the sine function, which is ƒ(x)=A*sin(B*(x−C))+D

A=9

B=1

C=0

3. Determine the amplitude by taking the absolute value of the coefficient A

Amplitude=|9|=9

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

Period=(2*π)/1=2*π

5. Identify the phase shift by looking at the horizontal displacement C

Phase Shift=0

Final Answer

Amplitude=9,Period=2*π,Phase Shift=0

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