Oh boy Oh boy

Nov 2019
A boat tied up at a dock bobs up and down with passing waves. The vertical distance between its high point and its low point is 1.8m and the cycle is repeated every 4 seconds.

a) Determine a sinusoidal equation to model the vertical position, in metres, of the boat versus the time, in seconds.

b) Use your model to determine when, during each cycle, the boat is 0.5m above its mean position. Round your answers to the nearest hundredth of a second.

How do you know if it is sin, cos, tan, sec, csc, or cot?
Also i'm kinda just lost for b
Solve in radians please


Forum Staff
Jan 2006
Wellsville, NY
a) If they are asking for a sinusoidal equation then it's either sine or cosine. I usually use the sine function if I'm given the choice, though many textbooks I've seen prefer cosine. It really doesn't matter.
\(\displaystyle y(t) = A~sin( \omega t )\) What is A? What is \(\displaystyle \omega\)?

b) y(t) = 0.5 m.

Give it a try and let us know what you come up with.