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((\pi)/(6))=(y)/(1)=y \\ \\ \\ \\ \cos((\pi)/(6))=(x)/(1)\rightarrow x \\ \\ \\ \\ [x,y]=[\cos((\pi)/(6)),\sin((\pi)/(6))]\rightarrow(1) \end{gathered}`

Simplifying equation (1) gives the following answer:

`\begin{gathered} [x,y]=[\cos((\pi)/(6)),\sin((\pi)/(6))] \\ \\ \\ \\ \sin((\pi)/(6))=(1)/(2) \\ \\ \cos((\pi)/(6))=(√(3))/(2) \\ \\ \\ \therefore\rightarrow \\ \\ [x,y]=[(1)/(2),(√(3))/(2)] \end{gathered}`

Therefore the answer is the second option.