Question

How do you find $\sin \left(-\frac{\mathrm{\pi }}{2}\right)$?

Answer 1

Use standard Trigonometric angles

We know that,

$\sin 90°=1$

The given expression is,

$\sin \left(-\frac{\mathrm{\pi }}{2}\right)=-\sin \frac{\mathrm{\pi }}{2}$ $\mathrm{[}\mathrm{\because }\mathrm{}\sin \left(-\theta \right)\mathrm{=}\mathrm{-}\mathrm{sin\theta }\mathrm{]}$

$\Rightarrow \sin \left(-\frac{\mathrm{\pi }}{2}\right)=-\sin \frac{180°}{2}$ $\mathrm{[}\mathrm{\because }\mathrm{}\mathrm{\pi }\mathrm{=}\mathrm{180}\mathrm{°}\mathrm{]}$

$\Rightarrow \sin \left(-\frac{\mathrm{\pi }}{2}\right)=-\sin 90°$

$\Rightarrow \sin \left(-\frac{\mathrm{\pi }}{2}\right)=-1$ $\mathrm{[}\mathrm{\because }\mathrm{}\sin \mathrm{90}\mathrm{°}\mathrm{}\mathrm{=}\mathrm{}\mathrm{1}\mathrm{]}$

Hence, the value of $\sin \left(-\frac{\mathrm{\pi }}{2}\right)$ is obtained to be $-1$, using the Trigonometric standard angle table.