Find Amplitude, Period, and Phase Shift f(x)=sec(x)

Problem

ƒ(x)=sec(x)

Solution

1. Identify the function type. The function ƒ(x)=sec(x) is the reciprocal of the cosine function, defined as 1/cos(x)

2. Determine the amplitude. For secant functions, there is no maximum or minimum value in the traditional sense because the range is (−∞,−1]∪[1,∞) Therefore, the amplitude is undefined.

3. Calculate the period. The period of sec(x) is the same as the period of cos(x) The standard formula for the period of sec(b*x−c) is (2*π)/|b| Since b=1 the period is 2*π

4. Find the phase shift. The phase shift is determined by the horizontal displacement in the argument (b*x−c) calculated as c/b Since the argument is simply x c=0 Thus, the phase shift is 0

Final Answer

Amplitude: Undefined, Period: *2*π*, Phase Shift: *0

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