Question

Given that sin θ = `a/b` then cos θ is equal to ______.

Options

• `b/sqrt(b^2 - a^2)`

• `b/a`

• `sqrt(b^2 - a^2)/b`

• `a/sqrt(b^2 - a^2)`

Answer 1

Given that sin θ = `a/b` then cos θ is equal to `underlinebb(sqrt((b^2 - a^2)/b)`.

Explanation:

According to the question,

sin θ = `a/b`

We know, sin² θ + cos² θ = 1

sin² A = 1 – cos² A

sin A = `sqrt(1 - cos^2 A)`

So, cos θ = `sqrt(1 - a^2/b^2)`

= `sqrt((b^2 - a^2)/b^2)`

= `sqrt(b^2 - a^2)/b`