Question

Find all the angles between 0° and 360° which satisfy the equation sin²θ = ${\displaystyle \frac{3}{4}}$

Answer 1

sin²θ = ${\displaystyle \frac{3}{4}}$

⇒ sin θ = ${\displaystyle \pm \frac{\sqrt{3}}{2}}$

sin 60° = ${\displaystyle \frac{\sqrt{3}}{2}}$

sin 120° = sin(180° – 60°)

= sin 60° 

= ${\displaystyle \frac{\sqrt{3}}{2}}$

∴ θ = 60° and 120°