Question

If tan θ = 3/4, then find the values of cos θ and sin θ.

Answer 1

Let,

The side opposite to angle θ =AB = 3k

The side adjacent to angle θ =BC = 4k

where k is any positive integer

Firstly we have to find the value of AC.

So, we can find the value of AC with the help of Pythagoras theorem

⇒ (AB)² + (BC)² = (AC)²

⇒ (3k)² + (4k)² = (AC)²

⇒ (AC)² = 9 k²+16 k²

⇒ (AC)² = 25 k²

⇒ AC =√25 k²

⇒ AC =±5k

But side AC can’t be negative. So, AC = 5k

Now, we will find the sin θ and cos θ

Side opposite to angle θ = AB = 3k

and Hypotenuse = AC = 5k