If the water must be at least 3m deep to dive safely, when during the daylight hours would it be safe to dive off the dock?

Question

The water at a local beach has an average depth at high tide of 8m. One cycle of the tides takes approximately 12 hours. This periodic motion can be modelled by the function d(t)=3.5cos[π/6 t]+4.5 where d(t) represents the depth of the water, in metres, at a time t, in hours. This equation assumes that the water level is at a high tide at time zero. Many people dive into the water from a nearby dock. If the water must be at least 3m deep to dive safely, when during the daylight hours would it be safe to dive off the dock? *YES THIS EQUATION IS RIGHT* sorry just had to say that because a lot of people think t is not supposed to equal zero. But high tide is at 8m.

Answer 1

3.5 cos [ pi/6 * t]+ 4.5 = 3

3.5 cos [ pi/6 * t] = -1.5

cos [ pi/6 *t] = -1.5/3.5 = -15/35 = -3/7

cosine is negative in quadrants 2 and 3...

arccos(3/7) = 64.623

so in degrees and in radians

117.377 2.0486151161133842275057205133289

244.423 4.266

4.266 hours --> 4 hours .266*60 = 16

2 am

4:16 am

2 pm

4:16 pm