Question

If $\sin \left(\theta \right)=0.3$, find the value of:

$\sin \left(\theta \right)+\sin \left(\theta +2\pi \right)+\sin \left(\theta +4\pi \right)$

Short answer

The value of$\sin \left(\theta \right)+\sin \left(\theta +2\pi \right)+\sin \left(\theta +4\pi \right)is0.9$

Step-by-step solution

Given information

We are given that$\sin \left(\theta \right)=0.3$

Use periodicity property of sine function sinθ+2π=sinθ

We get,

$$\begin{gathered} \sin \left(\theta \right)+\sin \left(\theta +2\pi \right)+\sin \left(\theta +4\pi \right) \\ \sin \left(\theta \right)+\sin \left(\theta \right)+\sin \left(\theta +2\pi \right) \\ \sin \left(\theta \right)+\sin \left(\theta \right)+\sin \left(\theta \right) \\ 3\sin \left(\theta \right) \\ 3(0.3) \\ =0.9 \end{gathered}$$

Conclusion 

The exact value of$\sin \left(\theta \right)+\sin \left(\theta +2\pi \right)+\sin \left(\theta +4\pi \right)is0.9$