Question

The value of $\cos {540}^{\mathrm{o}}$ is

Answer 1

Determine the value of $\cos {540}^{\mathrm{o}}$.

From the period formula of $\cos$ function, write the angle ${540}^{\mathrm{o}}$ as a sum or difference $2\mathrm{\pi n}$, where $n$ is the integer:

$$\begin{gathered} \cos {540}^{\mathrm{o}}=\cos ({180}^{\mathrm{o}}+{360}^{\mathrm{o}}) \\ =\cos {180}^{\mathrm{o}}...\left[\because cos(\theta +2\pi n)=cos\theta \right] \\ =-1 \end{gathered}$$

Hence, the required value $\cos {540}^{\mathrm{o}}=-1$.