Question

If sin A = ${\displaystyle \frac{3}{5}}$, then value of cot A is ______.

Options

• ${\displaystyle \frac{3}{4}}$

• ${\displaystyle \frac{4}{3}}$

• ${\displaystyle \frac{4}{5}}$

• ${\displaystyle \frac{5}{4}}$

Answer 1

If sin A = ${\displaystyle \frac{3}{5}}$, then value of cot A is ${\displaystyle \underline{\frac{4}{3}}}$.

Explanation:

We have sin A = ${\displaystyle \frac{3}{5}}$

As sin A = ${\displaystyle \frac{\text{p}}{\text{h}}}$

Let perpendicular = 3x and hypotenuse = 5x.

Also, let ABC be a right angled Δ.

5x	3x
A	B

AC = ${\displaystyle \sqrt{{\text{AB}}^2+{\text{BC}}^2}}$ (By using Pythagoras theorem)

${\displaystyle 5x=\sqrt{{\text{AB}}^2+{\left(3x\right)}^2}}$

(5x)² = AB² + 9x²

AB² = 25x² − 9x²

AB² = 16x²

⇒ AB = 4x

Thus, Base = 4x

Hence, cot A = ${\displaystyle \frac{\text{B}}{\text{P}}=\frac{4x}{3x}=\frac{4}{3}}$