Question

What values between $0^o$ and ${360}^o$ may $A$ have when
$\sin A=\frac{1}{\sqrt{2}}$

Answer 1

$\sin A=\frac{1}{\sqrt{2}}$

When $A$ is in first quadrant $\angle A={45}^{\circ }$

When $A$ is in second quadrant $\angle A={180}^{\circ }-{45}^{\circ }={135}^{\circ }$

In third and fourth quadrants $\sin A=\frac{1}{\sqrt{2}}$ will not be satisfied.$\because \sin A$ is negative in third and fourth quadrants.