Question

1) Find the angle in degrees without using a calculator: a) arcsin( √3/2)

Answer 1

$\begin{gathered} \frac{\sqrt[]{3}}{2}\text{ is a known value, and the main angle that has:} \\ \sin (\theta)=\frac{\sqrt[]{3}}{2}\text{ is }\theta=60\text{ degrees}=\frac{\pi}{3} \end{gathered}$

Then, since arcsin is a function:

$\begin{gathered} R\rightarrow\mleft\lbrace-1;\text{ 1}\mright\rbrace \\ We\text{ take only value }\theta=\frac{\pi}{3},\text{ without the periodic values.} \\ \text{That means,} \\ \arcsin (\frac{\sqrt[]{3}}{2})=60\text{ degrees= }\frac{\pi}{3} \end{gathered}$