Question

Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time? You must show all of your work.

Answer 1

Lol my name is Tammy.

1.) # of minutes: 55-20 = 35
fraction of the hour = 35/60 = .58333
# degrees of arc of the circle = 360 x .58333 = 210 degrees
# radians = 210*pi/180 = 3.665 radians

2.) Arc = (pi) x 2r x .58333
3.14 x 12 x .58333 = 21.98 in

3.) 5π inches = 5 x 3.14 = 15.708 inches / 6 in radius = 2.618 radians

4.) 2.618 radians * 180/pi = 150°
x coordinate = 6(cos 150°) = -5.196
y coordinate = 6(sin 150°) = 3
the coordinates would be (-5.196, 2)

Answer 2

Part1: 3.66519 radians

Part 2: 21.98 inches

Explanation:

In order to know how many radians did the minute hand move from 1:20 to 1:55 you just need to know that there are 60 minutes in a clock, and there are 360º in the same clock, so every minute that passes, the minute hand is advancing 6 degrees. And from 1:20 to 1:55 there are 35 minutes, so the answer to the grade that it advanced would be:

`35*6= 210 degrees`

now we just convert that into radians:

If 1 degree=0.0174 radians, how many radians will there be in 210?

`(0.0174)/(1)=(x)/(210)`

`x=((0.0174)(210))/(1)`

`x=3.555 radians`

Now to evaluate how much does it move we just have to calculate the circumference:

`c= diameter*\pi`

`c= 12*\pi`

`c= 37.68`

Now there are 37.68 inches in the whole circumferece, there are 60 minutes in that same circumference we just make a rule of three to know how many there are in 35 minutes:

`(37.68in)/(60)=(x)/(35)`

`x=((37.68in)(35))/(60)`

`x=21.98inch`