Question

A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12 radians?

Answer 1

Answer:

$\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}$

Step-by-step explanation:

The origin of the coordinate system is the center of the circle. So we have an angle that measures $5\pi/12=75^{\circ}$. so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

$x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})$

Finally, the exact value of the position of the rider after the carousel rotates $5\pi/12$ radians is:

$\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}$