Question
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.
Answers
GPT 3.5
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)
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)