Question

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`cosec theta = sqrt10`

Answer 1

consider a right-angled Δ^le ABC, we get

Let x be the adjacent side.

By applying Pythagoras theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

`(sqrt10)^2 = 1^2 + x^2`

x² = 10 − 1 = 9

x = 3

`sin theta = 1/cosec theta = 1/sqrt10`

`cos theta = "adjacent"/"hypotenuse" = 3/sqrt10`

`tan theta = "opposite sides"/"adjacebt side" = 1/3`

`sec theta = 1/cos theta = sqrt10/3`

`cot theta = 1/tan theta = (1/1)/3 = 3`