If sin θ = -(1/2) where θ lies between 180° and 360° then the value of θ will be

Question

If \(\sin \theta=-\frac{1}{2}\) where \(\theta\) lies between \(180^{\circ}\) and \(360^{\circ}\), then the value of \(\theta\) will be 

(A) \(210^{\circ}, 330^{\circ}\)

(B) \(150^{\circ}, 330^{\circ}\)

(C) \(210^{\circ}, 150^{\circ}\)

(D) None of these

Answer 1

Correct option is (A) \(210^{\circ}, 330^{\circ}\)   

The Sin function is negative in the third and fourth quadrants

\(\sin \theta = \frac{1}{2}\)   

\(\sin^{-1}(\frac{1}{2}) = 30^{\circ}\)

In the third quadrants, the angle is \(180^{\circ}+30^{\circ} = 210^{\circ} \)

In the fourth quadrants, the angle is \(360^{\circ} - 30^{\circ} = 330^{\circ}\)