A person is on the outer side of a carousel that is rotating counterclockwise. Using the unit circle to model the carousel, what is the exact position of the rider after the carousel rotates pi/12 radians.
Assuming the person starts at the point (1,0) on the unit circle (which represents the outer edge of the carousel), we can calculate their position after rotating counterclockwise by π/12 radians.
To rotate counterclockwise by π/12 radians, we need to find the point on the unit circle that is π/12 radians counterclockwise from the point (1,0).
Using the trigonometric identities cos(π/12) = cos(15°) = √6 + √2 / 4 and sin(π/12) = sin(15°) = √6 - √2 / 4, we can determine the position of the rider after rotating by π/12 radians to be:
(√6 + √2 / 4, √6 - √2 / 4)