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If $\cos \theta= 0.2$, find the value of:

$$\cos\theta + \cos (\theta + 2\pi) + \cos (\theta + 4\pi)$$

I got $0.6$ is this correct?

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    Cos has period $2\pi$ so... yes your are right but maybe you can supply more context... why is this interesting? – 2017-02-06

2 Answers 2

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Since $cos(\theta)$ is periodic every $2\pi$ or $360°$ $$cos(\theta)=cos(2n\pi+\theta)$$(adding any multiple of $2\pi$ to $\theta$)

thus making your equation equal to $3cos(\theta)=3\cdot 0.2=0.6$

So yes you are correct.

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You have to keep in mind that $cos$ is a periodic function (dependent on $\pi$ and $2\pi$), so for any values $k\in\mathbb{Z},\alpha\in\mathbb{R}$, $\cos(2k\pi + \alpha)$ = $\cos(\alpha)$.

Thus $\cos\theta$ = $\cos(\theta + 2\pi)$ = $\cos(\theta +4\pi)$ = 0.2. So their sum will be 0.6.