Question

an ocean grapher measured a set of waves during a storm and modelled the vertical displacement of waves using h(t)=0.6cos2t+0.8sint. Determine the vertical displacement of the wave when the velocity is 0m/s

Answer 1

the velocity is h'(t) = -1.2 sin2t+0.8cost
so, when is that zero?
t = π/2, sin^-1(1/3), π-sin^-1(1/3)
h(π/2) = -0.6 + 0.8 = 0.2
h(sin^-1(1/3)) = 0.6√8 + 0.8 * 1/3
h(π-sin^-1(1/3)) = -0.6√8 + 0.8 * 1/3

Answer 2

how do you know the function is at zero at sin^-1(1/3) and π-sin^-1(1/3) algebraically?

Answer 3

huh? You've forgotten your trig? Bad sign...
-1.2 sin2t+0.8cost = 0
-2.4 sint cost + 0.8 cost = 0
-0.8 cost (3sint - 1) = 0
cost = 0
sint = 1/3