Algebra questions

Question

A buoy bobs as the waves go past. The vertical displacement of the buoy with the respect to sea level can be modeled by y = 1.75 cos(pi/3) , where t is the time in seconds. Find the amplitude and the period. Interpret the amplitude and the period in the context of the problem. Graph the function.

Answer 1

The amplitude is 1.75( units not given) is the distance the buoy travels above and below sea level

period = 2pi/b= 2pi/(pi/3)= 6seconds which is the time it takes for it to complete

I am not able to draw the graph but I can give you the points which you can connect as a smooth cosine graph

Let the x axis be time and the y axis height. Divide the period of 6 seconds by 4 to get 1.5,

Since this is a cosine graph it will start at it maximum(1.75)

‘Points are (0.1.75) , (1.5,0) , (3,-1.75) , (4.5,0) and finally ( 6,1.75)

Connect these as a smooth cosine graph