# Math Help - wheel trig problem

1. ## wheel trig problem

A pebble is wedged in the bottom of a tire. The horizontal distance of the pebble from the left-most edge of the tire varies sinusoidally with the distance you have traveled. Diameter is 5pi inches

L=distance of the pebble from the left-most edge of the tire after you have traveled x inches. Write en equation relating L and X….work in degrees and radians? Degrees first I guess than convert…I dno.

Then…..determine the first positive x value that makes L = 1

2. Draw a picture, as you should do with all problems. Now, when the tire travels x inches forward, it means the circumference has moved along x inches. This means, that if the stone started at the bottom, it has now moved backwards by an angle θ relative to a vertical through the axis. The angle subtends a circumference of length x. The radius of the wheel is 2.5π inches. θ = arc length/radius = x/2.5π
Now, the pebble starts 5π inches to the right of the left most point. After the wheel goes forward x inches, the pebble moves back θ radians, so the distance backwards it moves is 5πsinθ inches (look at your diagram, draw a right angled triangle with hypotenuse equal to the radius of the wheel, when the stone has moved back by θ radians). So now the distance the stone is from the left most point, after it has moved forward x inches, is:
5π - 5πsinθ = 5π(1 - sinθ)
This is the distance L and we know θ = x/2.5π, so:
L = 5π[1 - sin(x/2.5π)]

I am sorry, I just can't seem to get this all the same font and size

3. that isnt right because you are not measuring the diagonal line from the leftmost point to the point where the pebble is now....that is L

4. Well that is simple; just construct another right-angled triangle and use some geometry.