Find Amplitude, Period, and Phase Shift y=sec(x)
Problem
Solution
Identify the function type. The function
y=sec(x) is the reciprocal of the cosine function, defined asy=1/cos(x) Determine the amplitude. For trigonometric functions like secant and cosecant, which have ranges of
(−∞,−1]∪[1,∞) there is no maximum or minimum value in the traditional sense. Therefore, the amplitude is undefined.Calculate the period. The period of the secant function is the same as the period of the cosine function. The standard formula for the period of
y=sec(B*x−C) is(2*π)/|B| SinceB=1 in this expression, the period is2*π Find the phase shift. The phase shift is determined by the horizontal displacement from the origin, calculated as
C/B In the expressiony=sec(1*x−0) bothC=0 andB=1 Thus, the phase shift is0
Final Answer
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