Question

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

`sin theta = 11/5`

Answer 1

We know `sin theta = "opposite side"/"hypotenuse" = 11/15`

Consider right-angled Δ^le ACB

Let x = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

By applying Pythagoras

𝐴𝐵² = 𝐴𝐶² + 𝐵𝐶²

225 = 121+𝑥²

𝑥² = 225 -121

𝑥² = 104

`x = sqrt104`

`cos = "adjacent side"/"hypotenuse" = sqrt(104/15)`

`tan = "opposite side"/"adjacent side" = 11/sqrt104`

`cosec theta = 1/sin theta = 15/11`

`sec = 1/cos theta = 15/sqrt104`

`cot = 1/ tan theta = sqrt104/11`