Question

The terminal side of an angle measuring radians intersects the unit circle at what point?

Answer 1

Answer: The following diagram illustrates the problem clearly:

Using trigonometric ratios, the following equations can be constructed:

$\begin{gathered} \sin(\frac{\pi}{6})=\frac{y}{1}=y \\ \\ \\ \\ \cos(\frac{\pi}{6})=\frac{x}{1}\rightarrow x \\ \\ \\ \\ [x,y]=[\cos(\frac{\pi}{6}),\sin(\frac{\pi}{6})]\rightarrow(1) \end{gathered}$

Simplifying equation (1) gives the following answer:

$\begin{gathered} [x,y]=[\cos(\frac{\pi}{6}),\sin(\frac{\pi}{6})] \\ \\ \\ \\ \sin(\frac{\pi}{6})=\frac{1}{2} \\ \\ \cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2} \\ \\ \\ \therefore\rightarrow \\ \\ [x,y]=[\frac{1}{2},\frac{\sqrt{3}}{2}] \end{gathered}$

Therefore the answer is the second option.