Suppose an angle sweeps out an arc length of 452 inches on a

Suppose an angle sweeps out an arc length of 4.52 inches on a circle with a radius of 3 inches.

a. What is the measure of the angle swept out (measured in radians)?

b. Assume the initial ray of the angle is in standard position (passing through the 3 o\'clock position) and the terminal ray swept counterclockwise, what is the horizontal displacement to the right of the vertical diameter (in radius lengths) of the arc\'s ending point?

c. Assume the initial ray of the angle is in standard position (passing through the 3 o\'clock position) and the terminal ray swept counterclockwise, what is the horizontal displacement to the right of the vertical diameter (in inches) of the arc\'s ending point?

Solution

a) R x angle = arc length

angle = 4.52/3 = 1.506667 radian

b) horizontal displacement = R(1 - cos1.506667) = 0.936R

c) = 2.808 in