If tan A= 4/3. Find the other trigonometric ratios of the angle A.

We know that,

Or

Here, θ = A

Let,

The side opposite to angle A =BC = 4k

The side adjacent to angle A =AB = 3k

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 A and cos A

Side opposite to angle A = BC = 4k

and Hypotenuse = AC = 5k

So,

Now, We know that

Side adjacent to angle A = AB = 3k

and Hypotenuse = AC = 5k

So,

Now, we find other trigonometric ratios