The height (ℎ, in metres) of the water at a certain point in a wave pool after � seconds, is modeled by the equation ℎ(t) = 2sin^2 t + sin t+ 2. Work in radians. Round to 2 decimals.

a) How high is the water after 3 seconds? (1 mark)

b) During the first 10 seconds, at what times does the wave height reach 3 metres? (5 marks)

1 answer

(a) just plug in t=3
(b) solve h(t) = 3
That is,
2sin^2 t + sin t+ 2 = 3
2sin^2 t + sin t - 1 = 0
(2sint-1)(sint+1) = 0
now finish it off