Can you explain how to solve this?

Question

Jennifer is riding on a merry-go-round at a carnival that revolves at a speed of 3.3 revolutions per minute. She is sitting 7 feet from the center of the merry-go-round. If Jennifer's starting position is 0 radians, what are her x- and y-coordinates after 57 seconds? 

Answer 1

(x, y) = (7cosθ, 7sinθ), where θ is the number of radians traveled along the circle of radius 7 feet in 57 seconds.

 

Speed of merry-go-round =

 

 

(3.3rev/min)(2πradians/1 rev)(1min/60sec) =

 

 

0.345575191rad/sec

 

So, θ = (57sec)(0.345575191rad/sec) = 19.69778594 radians

 

(x, y) = (7cos19.69778594, 7sin19.69778594) = (4.629, 5.251)