Question

Using the formula, $\sin A=\sqrt{\frac{1-\cos 2A}{2}}$ , find the value of sin 30°, it being given that cos 60° = $\frac{1}{2}$.

Answer 1

A = 30^o
⇒ 2A = 2 $\times$ 30^o = 60^o

By substituting the value of the given T-ratio, we get:

$$\begin{gathered} \sin A=\sqrt{\frac{1-\cos 2A}{2}} \\ \Rightarrow \sin {30}^o=\sqrt{\frac{1-\cos {60}^o}{2}}=\sqrt{\frac{1-{\displaystyle \frac{1}{2}}}{2}}=\sqrt{\frac{{\displaystyle \frac{1}{2}}}{2}}=\sqrt{\frac{1}{4}}=\frac{1}{2} \end{gathered}$$
∴ sin 30^o = $\frac{1}{2}$