Question

If sin A = `2/3`, then cos A is equal to ______.

Options

• `3/2`

• `sqrt(5)/3`

• `1/3`

• `1/sqrt(3)`

Answer 1

If sin A = `2/3`, then cos A is equal to `underlinebb(sqrt(5)/3)`.

Explanation:

sin A = `2/3`

We know that

sin² A + cos² A = 1

cos² A = 1 – sin² A

⇒ cos A = `sqrt(1 - sin^2A)`

⇒ cos A = `sqrt(1 - (2/3)^2`

⇒ cos A = `sqrt(1 - 4/9)`

⇒ cos A = `sqrt((9 - 4)/9`

= `sqrt(5/9)`

= `sqrt(5)/3`