Trigonometric Modelling

Figure 4 shows a sketch of a child's toy.
The toy consists of a specially weighted wheel that moves along the floor. The diameter if the wheel is 40cm.
An arrow is drawn on the wheel. At the instant when the wheel starts to move, the point of the arrow is 35 cm above the floor.
The wheel takes 2 seconds to complete one revolution.
The height above the ground, h centimetres, of the point of the arrow, t seconds after the wheel starts to move, is modelled by the equation.
h= |Acos(bt+a)°|

How do you find a complete equation for the model giving the exact value of A, the exact value of b, and the value of a to 3 sig fig?

I'm so lost any help would be appreciated

The complete question with diagrams is at
https://www.mymathscloud.com/api/download/modules/A-Level/Practice-Papers/Edexcel-Official/Shadow%20Papers/A-Level/JUNE%202022%20PURE%20SHADOW%20PAPER%202..pdf?id=148042316
For the model A would represent the (max) height of the particle, b would represent the angular speed and alpha would represent the offset at time 0. It should be relatively straightforward to get them from the given info about the diameter, initial position and the time period of the rotation.

So would A therefore be 40cm?
I don't wanna sound stupid but wdym but angular speed and the offset? I've never been taught those words.

This question part is all about mapping a basic sinusoidal function (cos) to circular motion. So as |cos|<=1, the particle could only reach h=40 (figure 5) if indeed A=40 so
|40cos()|<=40

Then its a case of thinking of how the time period (time for one complete revolution) is 2s.
|cos(t)|
repeats (one complete revolution) every t=180 seconds. So how can you scale t (use b) so that it repeats every 2s.

Then finally think about what the height is at t=0 and use simple trig to get the value of alpha as
h(0) = 40cos(alpha)

Thank you, that's quite helpful. One last question (sorry, I've really never learnt circular motion) but how do you know that |cos(t)| repeats every t=180 seconds? I don't get how you get there. However, I do now know b would therefore be 90

Normally cos(t) repeats every 360 (as the question is in degrees) as should be fairly obvious?
|cos(t)| has a restricted range and would take the values
1 at t=0,180,360y,...
0 at t=90,270,...
so its at the max height in the first case and hits the ground in the second case, so its at the max height every 180.

You should be able to do the question with just basic trig knowlelge and transformations. You dont really need to know much about circular motion and indeed modelling hitting the ground (height 0) as this one does is inappropriate, but thats beyond the question.

Ohh right yeah of course. I totally get it now, thank you this was really helpful!