In one of my high school maths questions the example given to find the maximum displacement of a Simple Harmonic Motion where $ x=2+4\cos \left (2t + \frac{\pi}{3} \right ) $ and the motion lies in the interval: $-2 \leq x\leq 6$ is:
- let $x=2+4\cos \left (2t + \frac{\pi}{3} \right )= 6$
- then $\cos \left (2t + \frac{\pi}{3} \right )= 1$
- $2t + \frac{\pi}{3} = 2\pi$
- $t = \frac{5\pi}{6}$
I am getting confused on the transition from line 2 to line 3. I'm confused as to how getting rid of the cos turns 1 into $2\pi$. Could someone please explain this at a high school level?