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Chapter 1: Problem 8

What is the domain of the secant function?

Short Answer

Expert verified
Answer: The domain of the secant function is all real numbers x except the odd multiples of 饾懃=\dfrac{(2n+1)\pi}{2}, where n is any integer. In interval notation, the domain of the secant function can be represented as: (-鈭�, 饾懃=\dfrac{\pi}{2}) 鈭� ( 饾懃=\dfrac{\pi}{2}, 饾懃=\dfrac{3\pi}{2}) 鈭� ( 饾懃=\dfrac{3\pi}{2}, 饾懃=\dfrac{5\pi}{2}) 鈭� ...

Step by step solution

01

Identify the secant function relationship with cosine function

We know that the secant function is the reciprocal of the cosine function: sec(x) = 1/cos(x).
02

Identify undefined values for cosine function

Cosine function only becomes undefined when its value is equal to zero, so we need to find the values of x when cosine(x) = 0.
03

Find the values of x where cosine(x) = 0

For the cosine function, the value becomes zero at odd multiples of \dfrac{\pi}{2}. That is, when x = \dfrac{(2n+1)\pi}{2}, where n is any integer.
04

Formulate the domain of the secant function

Since the secant function is undefined at the values of x mentioned in Step 3, the domain of the secant function is given by all real numbers x except the odd multiples of \dfrac{\pi}{2}. In interval notation, the domain of the secant function can be represented as: (-\infty, \dfrac{\pi}{2}) \cup (\dfrac{\pi}{2}, \dfrac{3\pi}{2}) \cup (\dfrac{3\pi}{2}, \dfrac{5\pi}{2}) \cup ...

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