Find Amplitude, Period, and Phase Shift f(t)=1/2*sec(t+2)-pi

Problem

ƒ(t)=1/2*sec(t+2)−π

Solution

1. Identify the standard form of the secant function, which is ƒ(t)=a*sec(b*(t−h))+k

2. Determine the amplitude. For the secant function, there is no amplitude in the traditional sense because the function is unbounded; however, the vertical stretch factor is |a|=|1/2|=1/2

3. Calculate the period using the formula P=(2*π)/|b| Since b=1 the period is P=(2*π)/1=2*π

4. Find the phase shift by solving the argument of the function for t Setting t+2=0 gives t=−2 This indicates a shift of 2 units to the left.

Final Answer

Amplitude: None (Vertical Stretch: 1/2*), Period: *2*π*, Phase Shift: −2

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