1. ## Modelling Trig Functions

Here is the question directly from the book:

A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 1.5 m above the floor (the peg is) and pushes it downward. The peg reaches a min height of 0.25 m and a max height of 2.75 m above the floor. Sketch two cycles of the graph representing the height above the ground as a function of the total distance moved. Then determine the equation of the sine function.

So I sketched it, (we are using radians now... Grade 12) and I have most of the equation except the horizontal shift...
y=-1.25sin(x- ?)+1.5

What is the question mark? I don't even know where to beign on that one...

Mike

2. you have the amplitude and vertical shift correct.

the height is a function of distance traveled, so the period is equal to one circumference ...

$T = 2.5\pi$

so ...

$B = \frac{2\pi}{2.5 \pi} = \frac{4}{5}$

now you have this ...

$y = -1.25\sin\left(\frac{4}{5}x + C\right) + 1.5$

if you think about it, you probably can reason why C = 0.

3. there we go. Thanks. I was mixing up the full angle of a cicle with the circumference of a circle in assuming hte circumference was 2pi .