Answer:
[tex]\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}[/tex]
Step-by-step explanation:
The origin of the coordinate system is the center of the circle. So we have an angle that measures [tex]5\pi/12=75^{\circ}[/tex]. so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:
[tex]x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})[/tex]
Finally, the exact value of the position of the rider after the carousel rotates [tex]5\pi/12[/tex] radians is:
[tex]\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}[/tex]
