Question

examine the angle and the point where the terminal side intersects the circle. what is the sine of the angle?

Answer 1

In order to find sin(theta), we need to find the sine of the red angle:

where the hypotenuse is given by

`\begin{gathered} c=\sqrt[]{(\frac{\sqrt[]{3}}{2}})^2+((1)/(2))^2 \\ c=\sqrt[]{(3)/(4)+(1)/(4)} \\ c=\sqrt[]{1} \\ c=1 \end{gathered}`

then, sine of this angle is equal to

`\sin \varphi=((1)/(2))/(1)=(1)/(2)`

On the other hand,

`\sin \theta=-\sin \varphi`

then, the answer is

`\sin \theta=-(1)/(2)`

which corresponds to option 3.