Chapter 13.6, Problem 4BCYP

To determine

To find the exact value of $\sin {420}^{\circ }$ .

Answer to Problem 4BCYP

  $\frac{\sqrt{3}}{2}$

Explanation of Solution

Given:

  $\sin {420}^{\circ }$

Calculation:

Given angle $\sin {420}^{\circ },$

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

  $\sin {420}^{\circ }=\sin \left({360}^{\circ }+{60}^{\circ }\right)$

  $\begin{array}{l}=\sin \left({60}^{\circ }\right)\\ =\frac{\sqrt{3}}{2}\end{array}$

Conclusion:

Therefore, the exact value of $\sin {420}^{\circ }$ is $\frac{\sqrt{3}}{2}$ .