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Chapter 1: Problem 7

Where is the tangent function undefined?

Short Answer

Expert verified
Answer: The tangent function is undefined at $$x=\frac{(2n+1)\pi}{2}$$ where n is an integer because the cosine function is equal to zero at these values and division by zero is undefined.

Step by step solution

01

Identify the denominator of the tangent function

The tangent function is given by tan(x) = sin(x)/cos(x). The denominator is the cosine function, cos(x).
02

Find values of x where cos(x) = 0

Cosine function, cos(x), is equal to zero at odd multiples of 蟺/2. Mathematically, this can be represented as: $$x=\frac{(2n+1)\pi}{2}$$ where n is an integer.
03

Recognize values of x where tangent function is undefined

Since division by zero is undefined, the tangent function is undefined when cos(x) = 0. Therefore, the tangent function is undefined at the values of x found in Step 2: $$x=\frac{(2n+1)\pi}{2}$$ where n is an integer.

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