Chapter 13.6, Problem 8CYU

To determine

To find the exact value of $\cos {540}^{\circ }$ .

Answer to Problem 8CYU

  $-1$

Explanation of Solution

Given:

  $\cos {540}^{\circ }$

Concept used:

Determine the quadrant in which the given trigonometric angle lies and solve.

Calculation:

Given angle $\cos {540}^{\circ },$

Remove full rotations of $360°$ until the angle is between $0°$ and $360°$ .

  $\cos {540}^{\circ }=\cos \left({360}^{\circ }+{180}^{\circ }\right)$

  $\begin{array}{l}=\cos {180}^{\circ }\\ =-1\end{array}$   [ $\because \cos {180}^{\circ }=-1$ ]

Conclusion:

Therefore, the exact value of $\cos {540}^{\circ }$ is $-1$ .