Hello, stones44!

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 the wheel has traveled. The diameter is inches.

= distance of the pebble from the leftmost edge of the tire.

= horizontal displacement of the wheel.

(a) Write an equation relating and

(b) Determine the first positive value that makesLet the radius beCode:* * * * * * * * * * E O * D *-+-------* * * : / | * : / θ | *: / | * C* - - - +A * * | * - - - - - * * * - - - - - - B

Let .

When the wheel has turned radians,

. . it has moved a distance equal to arc(BC): . .[1]

We see that: .

. . Hence: . .[2]

Substitute [1] into [2]: .

Since . we have: . .(a)

If , we have: .

. .

Therefore: . .(b)