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

Problem

y=csc(x)

Solution

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

2. Determine the amplitude. For the cosecant function, which is the reciprocal of the sine function, there is no amplitude in the traditional sense because the function does not have a maximum or minimum value; it extends to infinity.

3. Calculate the period using the formula P=(2*π)/|b| In this function, b=1

P=(2*π)/1

P=2*π

4. Identify the phase shift by looking at the horizontal displacement c In this function, there is no value subtracted from or added to x inside the function.

Phase Shift=0

Final Answer

Amplitude: None, Period: *2*π*, Phase Shift: *0

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