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4-89.

Circle with point in second quadrant, about 1 half up from negative x axis, segment connecting point to center, sector below radius & above negative x axis, shaded, counter clockwise arrow, from top of circle to left of circle, point on right end of horizontal diameter, labeled, P. On the midway of MathAmerica Carnival land is a wheel of fortune. A transparent wheel with a radius of one meter is in front of a shaded winning region that is stationary behind the wheel. Spin the wheel and if point P lands in the region, you win.

  1. If the point moves radians around the circle, how many degrees has it moved?

  2. Show the new position of the point after the rotation in part (a).

  3. The point has traveled a total of degrees. How far has it traveled?

  4. If the point rests in the shaded region when the wheel stops, the player wins. Will the player win?

Circle with point in second quadrant, about 1 half up from negative x axis, segment connecting point to center, sector below radius & above negative x axis, shaded, counter clockwise arrow, from top of circle to left of circle, point on right end of horizontal diameter, labeled, P.

Added to circle, green point P, in fourth quadrant, about 1 fifth up from negative y axis, and shaded central angle from positive x axis, even with green point P, labeled 286.5 degrees.

 number of times around the remainder.

That is short of the shaded region.

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