Chapter 4.2, Problem 6E

To determine

Write the names of the Trigonometric functions which are undefined when x = 0

Answer to Problem 6E

Tangent and Secant 

Explanation of Solution

Given:

Concept Used:

In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the propensity of assuming different values).

Calculation:

Any number divided by zero is always undefined; it is because we cannot find the value of the division.

In Trigonometry, $\tan \text{θ}=\frac{\text{y}}{\text{x}}=\frac{\text{y}}{\text{0}}=\text{Undefined}\&\sec \text{θ}=\frac{1}{\cos \text{θ}}=\frac{1}{\text{x}}==\frac{1}{0}=\text{Undefined}$

The tangent, and secant functions are the reciprocals of the cotangent, and cosine functions are undefined when x = 0.

Thus, the tangent, and secant functions are undefined when x = 0