Find Amplitude, Period, and Phase Shift y=csc(1/2x)

Problem

y=csc(1/2*x)

Solution

1. Identify the standard form of the cosecant function, which is y=a*csc(b*(x−h))+k In this equation, a=1 b=1/2 h=0 and k=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| Substituting b=1/2 gives P=(2*π)/(1/2)

4. Simplify the period calculation.

P=2*π⋅2=4*π

5. Identify the phase shift. The phase shift is determined by the value of h in the horizontal displacement. Since there is no value subtracted or added to x inside the function, the phase shift is 0

Final Answer

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

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