Chapter 13.6, Problem 7CYU

To determine

To find the exact value of $sin\left(-{60}^{\circ }\right)$ .

Answer to Problem 7CYU

  $-\frac{\sqrt{3}}{2}$

Explanation of Solution

Given:

  $sin\left(-{60}^{\circ }\right)$

Calculation:

Given angle $sin\left(-{60}^{\circ }\right),$

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

  $sin\left(-{60}^{\circ }\right)=-\sin {60}^{\circ }$   [ $\because \sin \left(-\theta \right)=-\sin \theta$ ]

  $=-\frac{\sqrt{3}}{2}$   [ $\because \sin {60}^{\circ }=\frac{\sqrt{3}}{2}$ ]

Conclusion:

Therefore, the exact value of $sin\left(-{60}^{\circ }\right)$ is $-\frac{\sqrt{3}}{2}$ .