Find Amplitude, Period, and Phase Shift y=2sec(1/2x-pi/3)

Problem

y=2*sec(1/2*x−π/3)

Solution

1. Identify the standard form of the secant function y=a*sec(b*x−c)+d where a=2 b=1/2 and c=π/3

2. Determine the amplitude. For the secant function, there is no amplitude in the traditional sense as the graph extends to infinity; however, the vertical stretch factor is |a|

|a|=|2|=2

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

P=(2*π)/(1/2)

P=4*π

4. Calculate the phase shift using the formula c/b

Phase Shift=(π/3)/(1/2)

Phase Shift=(2*π)/3

Final Answer

Amplitude: None (Stretch Factor: 2), Period: *4*π*, Phase Shift: (2*π)/3

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