Graph sec(x)

Problem

sec(x)

Solution

1. Identify the function as the reciprocal of the cosine function.

sec(x)=1/cos(x)

2. Determine the domain by finding where the denominator is zero. The function is undefined where cos(x)=0 which occurs at odd multiples of π/2

x=π/2+n*π

3. Identify vertical asymptotes at the values where the function is undefined.

x=…,−π/2,π/2,(3*π)/2,…

4. Determine the range based on the range of cos(x) which is [−1,1] Since sec(x) is the reciprocal, its values are always greater than or equal to 1 or less than or equal to −1

(−∞,−1]∪[1,∞)

5. Find key points by evaluating the function at specific angles. For example, when cos(0)=1 sec(0)=1 When cos(π)=−1 sec(π)=−1

(0,1),(π,−1),(2*π,1)

6. Sketch the curves between the vertical asymptotes. The graph consists of a series of "U-shaped" curves that open upward when cos(x)>0 and downward when cos(x)<0

Final Answer

sec(x)=1/cos(x)

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