Question

Which of the following trigonometric ratios has a value that is undefined?

Answer 1

In trigonometry, the tangent and secant ratios may become undefined; for tangent, this occurs at 90 degrees, as it involves division by zero.

Step-by-step explanation:

In trigonometry, which deals with the relationships between the angles and sides of right-angled triangles, some trigonometric ratios can become undefined for certain angle measures. For example, the tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. However, when the adjacent side is 0, as in the case of a 90-degree angle (right angle), the tangent becomes undefined since division by zero is undefined in mathematics. Similarly, the secant, which is the reciprocal of the cosine, can become undefined when the angle leads to a cosine of zero.

Answer 2

cosec
`\pi`

Step-by-step explanation:

Only two function cosec
`\pi` and cot
`\pi` of the five trigonometric function are undefined .

From the given option cosec
`\pi` is undefined as we know that

sin
`\pi` =0 and cosec is inverse of sin. So,

`cosec \pi =(1)/(sin\pi )\\cosec \pi =(1)/(0)  (sin \pi =0)\\ cosec \pi=` which is undefined.