Periodicity help

Hi, how could I find the period for each of these

1) x(t) = 8 sin 2t

Period = 2pi/ absolute 2 = pi ???

2 ) x(t) = 8 sin ^2(t)
3) x(t) = 8 sin 2t
4) x(t) = 2 |cos t|

BUMP

Well the period is the measure of how often it repeats.

\sin 2t

has a period of

\pi

since it's a stretch parallel to x axis scale factor 0.5 right , so the curve is 'squashed'. For the second one if you're having trouble use the identity

\cos 2t = 1-2\sin^2 t

and it should be a bit easier.
For the fourth one try sketching the curve.

Reply 3

LostGear

Original post by B_9710

Well the period is the measure of how often it repeats.

\sin 2t

has a period of

\pi

since it's a stretch parallel to x axis scale factor 0.5 right , so the curve is 'squashed'. For the second one if you're having trouble use the identity