Find Amplitude, Period, and Phase Shift y=csc(x/2)

Problem

y=csc(x/2)

Solution

1. Identify the standard form of the cosecant function y=a*csc(b*(x−c))+d In this equation, a=1 b=1/2 c=0 and d=0

2. Determine the amplitude. For the cosecant function, which is the reciprocal of the sine function, there is no maximum or minimum value in the traditional sense. Therefore, the amplitude is none or undefined.

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

4. Substitute the value of b into the period formula.

P=(2*π)/(1/2)

5. Simplify the expression to find the period.

P=4*π

6. Identify the phase shift. The phase shift is determined by the value of c Since there is no horizontal shift inside the argument of the function, the phase shift is 0

Final Answer

Amplitude: None, Period: *4*π*, Phase Shift: *0

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