The velocity function of a moving particle on a coordinate line is v(t) = 3cos(2t) for 0 is less than or equal to t
and 2pi is greater than or equal to t
(a) Determine when the particle is moving to the right.
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Obviously particle will move to the right when velocity is >0. cos x>0 implys that x is in 1st or 4th quadrant. So for your function that is for 0+k*2pi<=2t<pi/2+k*2pi and
where k is integer.
Deviding first inequality by 2 you get
0 + k*pi<=t<pi/4 + k*pi
and deviding second inequality by 2 you get
3pi/4 + k*pi <t<=pi + k*pi
So for k=0 and k=1 you get your solution.
Particle is moving ot the right when
t is from [0,pi/4] U [3pi/4,5pi/4] U [7pi/4,2pi].
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