Question

A toy racecar races along a circular race track that has a radius of 24 meters. The racecar starts at the 3-o'clock position of the track and travels in the CCW direction.

Suppose the racecar has traveled 56 meters along the race track.

How many radians has the racecar swept out?

2.33
Correct radians

What is the racecar's distance to the right of the center of the race track (in meters)?

-16.58
Correct meters

What is the racecar's distance above the center of the race track (in meters)?

17.35
Correct meters

Let
d
represent the racecar's varying distance traveled (in meters) along the circular race track.

Write an expression (in terms of
d
) to represent the racecar's distance to the right of the center of the race track (in meters).

24cos(d)


Write an expression (in terms of
d
) to represent the racecar's distance above the center of the race track (in meters).

24sin(d)
Is this correct if not correct me

Answer 1

The first few look good.
But when d is the distance around the track,
24cos(d) is not the correct answer
That is the value if d is the angle covered. But you should have
24 cos (d/24) because s=rθ, so θ = s/r

Answer 2

Doing 24COS(56) got me 13.42 not -16.58. What mistake did I make