Question

If sina = 3/5. Find the value of cosa and tana

Answer 1

Given that sin(a) = 3/5

We need to find cos(a).

First we will use trigonometric identities to find cos(a).

We know that:

sin^2 a + cos^2 a = 1

==> cos(a) = sqrt( 1- sin^2 a)

==> cos(a) = +-sqrt( 1- (3/5)^2 = sqrt( 1- 9/25) = sqrt 16/25 = 4/5

Then cos(a) = +- 4/5

And tana = 3/4

Answer 2

Let Triangle ABC be right angled at B and let AC be the hypotenuse

It is given that Sin A = 3/5.

Sin A = Opposite/Hypotenuse

So, Opposite = 3

     Hypotenuse = 5

By Pythagoras theorem,

AC² = AB² + BC²

⇒ 5² = 3² + AB²

⇒ 25 - 9 = AB²

⇒ √16 = AB = 4

∴ Cos A = Adjacent/ Opposite = 4/5

  Tan A = Opposite/ Adjacent = 3/4