Chapter 12.6, Problem 24PPS

To determine

To find the exact value of $\sin \left(-{45}^{\circ }\right)$ .

Answer to Problem 24PPS

  $\frac{1}{\sqrt{2}}$

Explanation of Solution

Given:

  $\sin \left(-{45}^{\circ }\right)$

Concept used:

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

  $\sin \left(-\theta \right)=\sin \theta$

Calculation:

Given angle $\sin \left(-{45}^{\circ }\right),$

Since $\sin \left(-\theta \right)=\sin \theta ,$

  $\sin \left(-{45}^{\circ }\right)=\sin \left({45}^{\circ }\right)$

  $=\frac{1}{\sqrt{2}}$

Conclusion:

Therefore, the exact value of $\sin \left(-{45}^{\circ }\right)$ is $\frac{1}{\sqrt{2}}$ .