Question

If sin²θ = `3/4`, then θ is ______.

Options

• 30°

• 45°

• 60°

• 90°

Answer 1

If sin²θ = `3/4`, then θ is 60°.

Explanation:

Given,

sin²θ = `3/4`

⇒ `sinθ = +- sqrt3/2`

⇒ `sinθ = sqrt3/2 "or" sinθ = - sqrt3/2`

sinθ = sin60°   ...(Since sin60°= `sqrt3/2`)

⇒ θ = 60°

(Case `sinθ = - sqrt3/2` is not included in our solution. because in this case θ > 90° and as per the syllabus we will restrict our discussion to acute angle and right angle only.)