Question

if sin tetha = 3/5,then cot tetha ​

Answer 1

✯ Solution :-

Given that ,

■ sinθ = 3/5

We need to find ,

■ cotθ = ?

If we need to find cotθ firstly we need to find cosθ & we should substitute in ,

• cotθ = cosθ/sinθ

Firstly finding cosθ using first trigonometric identity .

sin²θ + cos²θ = 1

Simplifying,

cosθ = ±√1 - sin²θ

Substituting the value of sinθ

➵ cosθ = ±√1 - [ 3/5 ]²

➵ cosθ = √1 - 9/25

➵ cosθ = √ 25 - 9/25

➵ cosθ = √16/25

➵ cosθ = 4/5

Now , finding cotθ

• cotθ = cosθ/sinθ

⇒ cotθ = (4/5)/(3/5)

⇒ cotθ = 4/3

Hence , cotθ = 4/3

Answer 2

Answer :-

Let, Perpendicular = AB = 3k

Hypotenuse = AC = 5k

where, k is any positive integer

So, by Pythagoras theorem,

we can find the third side of a triangle

⇒ (AB)² + (BC)² = (AC)²

⇒ (3k)² + (BC)² = (5k)²

⇒ 9k² + (BC)² = 25k²

⇒ (BC)² = 25k² – 9k²

⇒ (BC)² = 16k²

⇒ BC =√16k²

⇒ BC =±4k

But side BC can’t be negative.

But side BC can’t be negative. So, BC = 4k

Now, we have to find the value of cotθ

We know that,

$cotθ = \frac{Base}{Perpendicular}$

Base = BC = 4k

Perpendicular = AB = 3k

So, $cotθ = \frac{4k}{3k} = \frac{4}{3}$