Find Amplitude, Period, and Phase Shift y=sec(4x)

Problem

y=sec(4*x)

Solution

1. Identify the standard form of the function, which is y=a*sec(b*(x−c))+d For the given equation y=sec(4*x) the parameters are a=1 b=4 c=0 and d=0

2. Determine the amplitude. For the secant function, which is the reciprocal of cosine, there is no defined amplitude because the range is (−∞,−1]∪[1,∞) The vertical stretch factor is |a|=1

3. Calculate the period using the formula P=(2*π)/|b| Substituting b=4 gives P=(2*π)/4

4. Simplify the period expression to get P=π/2

5. Find the phase shift using the formula Phase Shift=c Since there is no horizontal shift inside the argument, the phase shift is 0

Final Answer

Amplitude: None, Period: π/2*, Phase Shift: *0

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