What function rule

Question

The motion of a yo-yo is represented by a sine function. A trick rotates the yo-yo 6 times in a total of 2π seconds. What function rule could model this situation?

Answer 1

Does the answer specifically have to be in the form of a sine function? If not:

1. A single rotation covers 2π radians

1. So 6 rotations cover 12π radians

1. To determine how many radians the yo-yo covers per second:

Radians covered / total time = 12π radians / 2π seconds = 6 radians per second

1. To express this in terms of rotations per second divide the above answer by 2π

Giving 6/2π rotations per second

1. Bringing all of this together,
2. If t represents the number of seconds since the beginning of the trick
3. f(t) = 6t/2π is the number of rotations completed by the yo-yo

I hope this helps