Given the graph of y=cos(θ + pi/2) from 0 ≤ θ ≤ 2π:

Question

a) For what value(s) of θ does the instantaneous rate
of change appear to equal 0?

b) For what value(s) of θ does the instantaneous rate of change reach its maximum? Its minimum?

Thank you!

Answer 1

to make things easier, note that
y=cos(θ + pi/2) = -sinθ

The tangent lines are horizontal at the max/min points, where sinθ = ±1

The slope is greatest/least where sinθ=0