Question

Find the value of $\sin {270}^{\circ }$.

Answer 1

Find the value given trigonometric expression.

Given, $\sin {270}^{\circ }$can be expressed as, $\sin {270}^{\circ }=\sin ({180}^{\circ }+{90}^{\circ })$

Since $$\sin$$ is a periodic function of time period $$2\pi$$, also negative in third quadrant or $\sin (\pi +\theta )=-\sin \theta$,where$\pi ={180}^{\circ }$

Therefore,

$$\begin{gathered} \sin {270}^{\circ }=\sin ({180}^{\circ }+{90}^{\circ }) \\ =-\sin {90}^{\circ } \\ =-1 \\ \therefore \sin {270}^{\circ }=-1 \end{gathered}$$
Hence, the value of $\sin {270}^{\circ }$is$-1$.