Question

I really need help solving thisIt’s from my ACT prep guide 21’-22’

Answer 1

Coterminal angles: are angles in standard position (angles with the initial side on the

positive x-axis) that have a common terminal side.

If we call our angle as θ, its coterminal angles are given by

`\begin{gathered} \theta\pm2\pi n \\ n\in\mathbb{N} \end{gathered}`

Our angle is 4π/3, therefore, its coterminal angles are

`\begin{gathered} (4\pi)/(3)\pm2\pi n=\ldots,(4\pi)/(3)-4\pi,(4\pi)/(3)-2\pi,(4\pi)/(3),(4\pi)/(3)+2\pi,(4\pi)/(3)+4\pi,\ldots \\ =\ldots,-(8\pi)/(3),-(2\pi)/(3),(4\pi)/(3),(10\pi)/(3),(16\pi)/(3),\ldots \end{gathered}`

From the given options, those that fits this description are

`-(8\pi)/(3),-(2\pi)/(3),(10\pi)/(3)`