$\text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. }$
A) 0
B) $\frac { 3 \pi } { 2 }$
C) $\frac { 7 \pi } { 2 }$
D) $\frac { \pi } { 6 }$
E) $\frac { 4 \pi } { 5 }$

Question

$\text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. }$ 
A) 0
B) $\frac { 3 \pi } { 2 }$
C) $\frac { 7 \pi } { 2 }$
D) $\frac { \pi } { 6 }$
E) $\frac { 4 \pi } { 5 }$

Quizplus · Accepted Answer

By definition, $\arcsin 	heta$ is the angle $\alpha$ such that $\sin \alpha = 	heta$ and $-\frac{\pi}{2}\le \alpha \le \frac{\pi}{2}$. Since $\sin \frac{\pi}{6} = \frac{1}{2},$ we have $\arcsin \left(\frac{1}{2}ight) = \boxed{\frac{\pi}{6}}.$

Evaluate the expression arcsin⁡(12) without using a calculator. \text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. } Evaluate the expression arcsin(21​) without using a calculator.

$\text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. }$