Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

`tan alpha = 5/12`

Answer 1

`tan alpha = 5/12`

We know that `tan alpha ="opposite side/adjacent side"= 5/12`

Now consider a right-angled Δ^le ABC

Let x = hypotenuse .By applying Pythagoras theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

𝑥² = 52 + 122

𝑥² = 25 + 144 = 169

𝑥 = 13

`sin α = "adjacent side"/"hypotenuse"= 5/13`

`cos α =  "adjacent side"/"hypotenuse" = 12/13`

cot α = `1/tan alpha = 12/15``

cosec α = `1/sin alpha = (1/5)/13 = 13/5`

sec α = `1/cos alpha = (1/12)/13 = 13/12`