So I'm taking pre-calc currently and I am incredibly stumped and in a hurry on these questions. I'd love some help with a detailed step process so I can understand it. Please and thanks!

1. Sketch y= -4+2 cos3(x-pi) Explain the amplitude, period, and translations.

I guess that because (y-k) is the standard equation for the problem that the -4 would mean it shifts down four units. My main problem with this is I've seen other problems where the number in front that's being added to the 2cos/sin3 problems is that it is usually the middle point of the max and min. Is that true for this one as the graph I'm provided does not indicate that it goes down that far. I have no idea what the translations mean. Also would x-pi mean that it shifts to the right one pi?

3. A reflector is attached to the front wheel of a bike 20 cm away from the center of the wheel. The diameter of the wheel and tube is 70cm. The bike is going 10 km/hr, express the height of the reflector above me the ground as a function of time. Assume time is t=0 seconds. Reflector starts at the highest point.

This question was probably the hardest for me. I understand that this would basically be a cosine graph starting at the top, I know the radius is 35 cm so the highest the reflec can go is 55 cm and the lowest it can go is 15cm. My only problem is how am I supposed to know how long the period is? I have all the numbers for the graph except for how long it takes a full revolution from the reflector to go from the top all the way around and back to the top.

Once again please and thanks!

Changelog:

1. Posted work

2. Solved #2 by myself.