Find Amplitude, Period, and Phase Shift y=sec(x/3)

Problem

y=sec(x/3)

Solution

1. Identify the standard form of the function. The given function is in the form y=a*sec(b*(x−h))+k where a=1 b=1/3 h=0 and k=0

2. Determine the amplitude. For the secant function, which is the reciprocal of cosine, there is no amplitude in the traditional sense because the function is unbounded. However, the vertical stretch factor is |a|=1

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

P=(2*π)/(1/3)

P=6*π

4. Identify the phase shift by looking at the horizontal displacement h Since there is no value subtracted from x inside the function, the phase shift is 0

Final Answer

Amplitude: None, Period: *6*π*, Phase Shift: *0

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