Find Amplitude, Period, and Phase Shift f(x)=sin(x/3)

Problem

ƒ(x)=sin(x/3)

Solution

1. Identify the standard form of the sine function, which is ƒ(x)=a*sin(b*(x−h))+k

2. Determine the coefficients from the given function ƒ(x)=1*sin(1/3*x) where a=1 b=1/3 h=0 and k=0

3. Calculate the amplitude using the formula |a|

|1|=1

4. Calculate the period using the formula (2*π)/|b|

(2*π)/1/3=6*π

5. Determine the phase shift using the value of h

h=0

Final Answer

Amplitude=1,Period=6*π,Phase Shift=0

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