Question

If $\cos \mathrm{\theta }=-\frac{1}{2}\mathrm{and}0<\mathrm{\theta }<360°$, then the solutions are
(a) $\theta =60°,240°$
(b) $\theta =120°,240°$
(c) $\theta =120°,210°$
(d) $\theta =120°,300°$

Answer 1

(b) $\theta =120°,240°$

Given equation:
$$\begin{gathered} \cos \theta =-\frac{1}{2} \\ \Rightarrow \cos \theta =\cos 120° \\ \Rightarrow \theta =120° \end{gathered}$$
Or,
$$\begin{gathered} \cos \theta =\cos 240° \\ \Rightarrow \theta =240° \end{gathered}$$

So, both $120°\mathrm{and}240°$ lie in $0<\theta <360°$.