Question

if$\cos \left(\theta \right)=0.2$, then find the value of$\cos \left(\theta \right)+\cos \left(\theta +2\pi \right)+\cos \left(\theta +4\pi \right)$

Short answer

The exact value of$\cos \left(\theta \right)+\cos \left(\theta +2\pi \right)+\cos \left(\theta +4\pi \right)is0.6$

Step-by-step solution

Given information

We are given that$\cos \left(\theta \right)=0.2$

Use periodicity of trigonometric function cosθ+2π=cosθ

We get,

$$\begin{gathered} \cos \left(\theta \right)+\cos \left(\theta +2\pi \right)+\cos \left(\theta +4\pi \right) \\ \cos \left(\theta \right)+\cos \left(\theta \right)+\cos \left(\theta +2\pi \right) \\ \cos \left(\theta \right)+\cos \left(\theta \right)+\cos \left(\theta \right) \\ 3\cos \left(\theta \right) \\ =3(0.2) \\ =0.6 \end{gathered}$$

Conclusion

The value of$\cos \left(\theta \right)+\cos \left(\theta +2\pi \right)+\cos \left(\theta +4\pi \right)is0.6$