Question

How do I find the value of $\sin \left(225°\right)$.

Answer 1

Calculate the value of $\sin \left(225°\right)$:

First, determine the sign of $\sin \left(225°\right)$.

$225°$ can be rewritten as $225°=180°+45°=\left(2\times 90°\right)+45°$.

Thus $225°$ belongs to the third quadrant.

It is known that the values of sines are negative $\left(-\right)$ in the third quadrant.

It is also known that, $\sin \left(180°+x°\right)=-\sin \left(x°\right)$.

Thus, $\sin \left(225°\right)=\sin \left(180°+45°\right)=-\sin \left(45°\right)=-\frac{1}{\sqrt{2}}$.

Therefore, the value of $\sin \left(225°\right)$ is $-\frac{1}{\sqrt{2}}$.