Find Amplitude, Period, and Phase Shift y=1-1/2*sin(3x-pi/4)

Problem

y=1−1/2*sin(3*x−π/4)

Solution

1. Identify the standard form of the trigonometric function y=d+a*sin(b*x−c) where |a| is the amplitude, (2*π)/b is the period, and c/b is the phase shift.

2. Determine the amplitude by taking the absolute value of the coefficient of the sine function.

|a|=|−1/2|=1/2

3. Calculate the period using the formula P=(2*π)/b where b=3

P=(2*π)/3

4. Find the phase shift by setting the argument of the sine function to zero and solving for x or using the formula c/b

3*x−π/4=0

3*x=π/4

x=π/12

Final Answer

Amplitude=1/2,Period=(2*π)/3,Phase Shift=π/12

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