I am having trouble figuring out this question
Jan observes a buoy bobbing up and down through a total amplitude of 8 feet. Beginning at the top of the wave, if the buoy completes a full cycle every 8 seconds, what is the height of the buoy relative to its lowest point after 12 seconds?
I tried making a function out of what was given to me but I am missing so much information I don't understand dhow it would work.
amplitude=1/2 full swing=4feet
period = 8 seconds, or freq=1/8 second, or w=2PI/8 or PI/4 rad/sec
h=4cos(wt)=4cos(PI/4 * 12)=4cos 3PI
check that.
another way: the time is 1.5 periods, which means it has to be on the lowest point.
sketch the graph
where did the 12 come from?
oops sorry never mind
How do you know to use cos and not sine?
cos has value of 1 at t = 0 so that would be at the top of the wave as the problem stated.
Sin of 0 is 0 so that is not what you want.
You could do the same thing with a phase shift of pi/2 because
sin (90 deg -a) = cos a
sin (pi/2 - pi t/4) = cos (pi t/4)