Finding ratios when other ratios are given

If sin A = 5/13. Find cos A, tan A, cosec A, sec A, cot A

sin A = 5/13

 (side opposite  to  ∠A)/Hypotenuse = 5/13

 ⇒ BC/AC = 5/13

Let

      BC = 5x

      AC = 13x

We find AB using Pythagoras Theore

In Δ ABC, using Pythagoras theorem

(Hypotenuse) ² = (Height) ² + (Base) ²

  AC ² = AB ² + BC ²

  (13x) ² = AB ² + (5x) ²

  169x ² = AB ² + 25x ²

  169x ² – 25x ² = AB ²

  144x ² = AB ²

  AB ² = 144x ²

  AB = √144x ²

  AB = √144 x

  AB = 12x

So, our triangle becomes

Now, we find cos A & tan A

Now, let us find cosec, cot and tan