Question

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

`cos A = 4/5`

Answer 1

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

Let us consider a right-angled ΔABC

 

Let opposite side BC = x.

By applying Pythagoras theorem, we get

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

25 = x + 16

x = 25 - 16 = 9

x = `sqrt9 = 3`

We know that `cosA = 4/5`

`sin A = "opposite side"/"hypotenuse" = 3/5`

`tan A = "opposite side"/"adjacent side"  = 3/4`

`cosec A = 1/(sin A) = (1/3)/5 = 5/3`

`sec A = 1/(cos A) = (1/4)/5 = 5/4`

`cot A = 1/(tan A) =(1/3)/4 = 4/3`