Answer:
The point [tex](\frac{\sqrt{3}}{2},-\frac{1}{2})[/tex]
Step-by-step explanation:
I added a graphic to the explanation.
Given the unit circle (the circle with radius equal to 1 unit centered at the point (0,0) ) we can represent its points only with an angle.
The point [tex]-(\frac{\pi}{6})[/tex] corresponds to the point that forms an angle of -30° respect to the positive axis-x (we measure the positive angles counterclockwise respect to the positive x-axis and the negative angles clockwise) because [tex]-(\frac{\pi}{6})[/tex] it is in radians and 180° = π radians ⇒
-(π/6) = - (180°/6) = - 30°
Given that we identify the point on the graph, we can find it coordinates using sine and cosine function :
[tex]sin(-30)=\frac{y1}{1} \\y1=-0.5=-\frac{1}{2}[/tex]
[tex]cos(-30)=\frac{x1}{1} \\x1=\frac{\sqrt{3}}{2}[/tex]
It is important to note that the hypotenuse of the right triangle which we used to apply sine and cosine is equal to 1 because is the radius of the unit circle.
The coordinates of the point are [tex](x1,y1)=(\frac{\sqrt{3}}{2},-\frac{1}{2})[/tex]
