Question

If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are

Options

• \[x = \frac{\pi}{3}, \frac{4\pi}{3}\]

   

• \[x = \frac{2\pi}{3}, \frac{4\pi}{3}\]

   

• \[x = \frac{2\pi}{3}, \frac{7\pi}{6}\]

   

• \[\theta = \frac{2\pi}{3}, \frac{5\pi}{3}\]

   

Answer 1

\[x = \frac{2\pi}{3}, \frac{4\pi}{3}\]
Given equation:
\[\cos x = - \frac{1}{2}\]
\[ \Rightarrow \cos x = \cos \frac{2\pi}{3}\]
\[ \Rightarrow x = \frac{2\pi}{3}\]
Or,
\[\cos x = \cos \frac{4\pi}{3}\]
\[ \Rightarrow x = \frac{4\pi}{3}\]

So, both 

\[\frac{2\pi}{3} \text{ and }\frac{4\pi}{3}\] lie in

\[0 < x < 2\pi\].