Question

Using the trigonometric definitions for any angle theta​, the trigonometric functions that are undefined when x = 0 are​ ______ and​ _______. The trigonometric functions that are undefined when y = 0 are​ _______ and​ _______. The trigonometric functions that do not depend on the value of r are​ _______ and​ _______.

Answer 1

Answer: Using the trigonometric definitions for any angle theta​, the trigonometric functions that are undefined when x = 0 are​ tanθ and secθ. The trigonometric functions that are undefined when y = 0 are cotθ and​ cscθ. The trigonometric functions that do not depend on the value of r are​ tanθ and​ cotθ.

Step-by-step explanation:

Construct a trigonometric ratio for triangle and you will see that cot and tan are independent of the value, r.

NOTE: A ratio is undefined if the denominator is zero.

Also, from that trigonometric ratio constructed, if x=0, only tanθ and secθ become undefined. And if y=0, only cotθ and cscθ become undefined.

The attachment below shows a constructed trigonometric ratio.