Answer:
see below
Explanation:
Factor the equation and use the zero product rule.
0 = 2sin(t)² +sin(t) . . . . . . . the velocity is zero
0 = sin(t)·(2sin(t) +1) . . . . . factor the equation
The product will be zero when either factor is zero:
sin(t) = 0
This is true for t = 0, π, 2π.
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2sin(t) +1 = 0
This is true for sin(t) = -1/2, at t = 7π/6 and 11π/6.
Then the solution is ...
t ∈ {0, π, 7π/6, 11π/6, 2π}