What is the Angle of a Dust Speck on a Turntable After 8 Seconds?

[Sylis]

Homework Statement

A turntable rotates counterclockwise at 78rpm, a speck of dust on the turntable is at 0.42rad at t=0 ,What is the angle of the speck at t = 8.0s ? Your answer should be between 0 and 2π rad
Express your answer using two significant figures.

Homework Equations

θ_f-θ_i=ωt

The Attempt at a Solution

I missed a couple of classes so I'm incredibly behind. I've been trying to google how to do things but it's not really working out for me, so if something is wrong let me know (which it obviously is or I wouldn't be here).

So, I started out by converting the 78 rpm measurement into an angular velocity

78rpm x 2∏ x 1/60 = 8.168rad/s

Then by using the formula for Δθ (θ_f-θ_i=ωt)
θ_f=ωt+θ_i

8.168(8)+0.24rad = 65.585 rad.

I've tried 66 rad and 65 rad just to see if that helped at all, but to no avail. I know it says that my answer is supposed to be between 0 and 2pi and that 65.5 is far larger than 2pi, what else am I supposed to do?

I've done my best at the problem... I don't know what else to do.

 

[nasu]

A full rotation is 2∏ radians.
After a full rotation the speck is back where is was. So you need to find what is the closest multiple of 2∏ (but lower than your result) and take only what is left over.
For example if your result would be 10 radians, the closest multiple is 6.28 (2 ∏) so the angle of displacement will be 10-6.28= 3.72 rad.

 

[Sylis]

I got it, 65.585- (2pi x 10) = 2.9 rad.

Thank you. I'm having a real tough time with these problems.