Question

Grade 12 math: Trig identities/equations?
the depth of the ocean at a swim buoy can be modelled by the function d(t) = 4 + 2sin[(pi/6)t], where d is the depth of the water in metres and t is the time in hours, if t is between 0 and 24. Consider a day when t=0 represents midnight. Determine when the depth of water is 3m.

answer: t=7, 11, 19, and 23

How do you solve this question? I don't get it.. I got until sin[(pi/6)t] = -1/2...

Answer 1

d = 3 = 4 +sin(pi*t/6)
sin (pi*t/6) = -1
pi*t/6 = 3*pi/2 or 7*pi/2
t = 9 or t = 21

Answer 2

There's a 2 in front of sin(pi*t/6) though :S

Answer 3

Dang: pi*t/6 = 11pi/6 or 7pi/6 or 23pi/6 or 19pi/6
t = 7,11,19, or 23

Answer 4

Thanks :)