Q.89 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The value of $\sin \left(\theta \right)+\sin \left(\theta +2\pi \right)+\sin \left(\theta +4\pi \right) is 0.9$

Step 1: Given information

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

Step 2: Use periodicity property of sine function sin θ + 2 π = sin θ

We get,

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

Step 3: Conclusion

The exact value of $\sin \left(\theta \right)+\sin \left(\theta +2\pi \right)+\sin \left(\theta +4\pi \right) is 0.9$