Question

I am so confused! Can anyone help me with this trig problem?

Answer 1

$\frac{5\pi }{4}$ or $\frac{7\pi }{4}$

divide both sides by 2

sinΘ = - $\frac{\sqrt{2} }{2}$

Since the sin ratio is negative then Θ is in third / fourth quadrants

Θ = $sin^{- 1}$ ($\frac{\sqrt{2} }{2}$) = $\frac{\pi }{4}$ related acute angle

Θ = ( π + $\frac{\pi }{4}$ ) = $\frac{5\pi }{4}$

or Θ = ( 2π - $\frac{\pi }{4}$ ) = $\frac{7\pi }{4}$