Find Amplitude, Period, and Phase Shift y=-sin(4x)

Problem

y=−sin(4*x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=−1 The amplitude is the absolute value |A|

|A|=|−1|=1

3. Determine the value of B to find the period. Here, B=4 The formula for the period of a sine function is (2*π)/B

Period=(2*π)/4

4. Simplify the period fraction.

Period=π/2

5. Identify the phase shift C Since the expression inside the sine function is 4*x which can be written as 4(x - 0),t*h*e*v*a*l*u*e*o*ƒi*s()$.

Phase Shift=0

Final Answer

Amplitude=1,Period=π/2,Phase Shift=0

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