the minute hand of a clock is 6 inches long.how far does the tip of the minute hand move in 15 minutes?how far does it move in 25 minutes?

Question

it's a question for homework from my calculus class. I knoe its  trigonometry but the degrees on the unit circle confuse me. I think some equations are s=rθ, A=1/2r^2θ, ^_or A=θ/360×πr^2

Answer 1

The circumference of a circle with radius 6 inches is 12π inches.

 

15 minutes is 1/4 of the circle which is 60 minutes

 

Therefore the tip moves 1/4 of 12π = 3π inches

 

In 25 minutes the tip moves (25/60)12π = 5π inches

 

Yes, you can also use the formula s = rθ

 

θ is the angle of rotation. 15 minutes is equivalent to 90 degrees or π/2 radians

 

Therefore s = 6 inches(π/2) = 3π inches

 

25 minutes is equivalent to 25/60 x 360 degrees = 150 degrees = 5π/6 radians