Q.93 - Precalculus Enhanced with Graphing Utilities

Question

Find the exact value of $\sin \left(1^o\right)+\sin \left(2^o\right)+\sin \left(3^o\right)+....+\sin \left({360}^o\right)$

Step-by-Step Solution

Answer

The exact value of $\sin \left(1^o\right)+\sin \left(2^o\right)+....+\sin \left({360}^o\right)$ is $0$

Step 1: given information

We are given $\sin \left(1^o\right)+\sin \left(2^o\right)+....+\sin \left({360}^o\right)$

Step 2: Use periodicity property sin θ = sin θ - 2 π

We get

$$\begin{gathered} \sin \left(1^o\right)+\sin \left(2^o\right)+....+\sin \left({360}^o\right) \\ \sin \left(-{359}^o\right)+\sin \left(-{358}^o\right)+....+\sin \left({360}^o\right) \\ -\sin \left({359}^o\right)-\sin \left({358}^o\right)-....+\sin \left({360}^o\right) \\ =0 \end{gathered}$$

Step 3: Conclusion

The exact value of $\sin \left(1^o\right)+\sin \left(2^o\right)+....+\sin \left({360}^o\right) is 0.$