Find Amplitude, Period, and Phase Shift y=-csc(3x-pi)

Problem

y=−csc(3*x−π)

Solution

1. Identify the general form of the cosecant function, which is y=a*csc(b*(x−h))+k or y=a*csc(b*x−c)+d

2. Determine the amplitude. For the cosecant function, there is no amplitude in the traditional sense because the range is (−∞,−1]∪[1,∞) However, the absolute value of the coefficient a is often referred to as the vertical stretch factor.

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

4. Find the phase shift by setting the argument of the function to zero: 3*x−π=0 Solve for x to find the horizontal displacement.

Final Answer

Amplitude: None (Vertical Stretch: 1)

Period=(2*π)/3

Phase Shift=π/3

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