Find Amplitude, Period, and Phase Shift y=sin(7x)

Problem

y=sin(7*x)

Solution

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

2. Determine the amplitude by finding the absolute value of the coefficient A in front of the sine function.

|A|=|1|=1

3. Calculate the period using the formula P=(2*π)/|B| where B is the coefficient of x

B=7

P=(2*π)/7

4. Find the phase shift by identifying the horizontal displacement C Since there is no constant added or subtracted inside the argument of the sine function, the shift is zero.

C=0

Final Answer

Amplitude=1,Period=(2*π)/7,Phase Shift=0

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