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Question
If \[\cos x = - \frac{3}{5}\] and x lies in IInd quadrant, find the values of sin 2x and \[\sin\frac{x}{2}\] .
Solution
\[ \Rightarrow \text{ sin } x = \pm \frac{4}{5}\]
Here, x lies in the second quadrant.
\[ \Rightarrow 2 \sin^2 \frac{x}{2} = 1 - \left( - \frac{3}{5} \right) = \frac{8}{5}\]
\[ \Rightarrow \sin^2 \frac{x}{2} = \frac{4}{5}\]
\[ \Rightarrow \sin\frac{x}{2} = \pm \frac{2}{\sqrt{5}}\]
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