trigonometric functions

Question

The minute hand of a clock is 6 inches long and moves from 3 o'clock to 5 o'clock. How far does the tip of the minute hand move? Express your answer round to two decimal places.

Answer 1

s = arc length (distance traveled by the tip of the minute hand)

r = radius of the clock

θ = measure of central angle (in radians)

 

in two hours, the angle swept out by the minute hand is 2/12 of a complete rotation

 

θ = (2/12)(2π) = π/3

 

s = rθ = 6(π/3) = 2π = 6.28 inches