Question

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

`cos theta = 7/25`

Answer 1

We know that `cos theta = "adjacent side"/"hypotence"`

Now consider a right-angled Δ^le ABC

Let x be the opposite side.

By applying Pythagoras theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

(25)² = 𝑥² + 7²

625 - 49 = 𝑥²

`576 = sqrt576 = 24`

`sin theta = "opposite side"/"hypotenuse"= 24/25`

`tan theta = "opposite side"/"adjacent side" = 24/7`

`cosec theta = 1/sin theta = (1/3)/5 = 25/24`

`sec theta = 1/cos theta = (1/4)/5 = 25/7`

`cot theta = 1/tan theta = (1/3)/4 = 7/24`