Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-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 3:35 to 3:55? (Hint: Find the number of degrees per minute first.)

Part 2: How far does the tip of the minute hand travel during that time?

Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 3π inches?

Part 4: What is the coordinate points associated with this radian measure?

Question

Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-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 3:35 to 3:55? (Hint: Find the number of degrees per minute first.)

Part 2: How far does the tip of the minute hand travel during that time?

Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 3π inches?

Part 4: What is the coordinate points associated with this radian measure?

anonymous · Answer

First step is to find how many degrees there are per minute. 60 minutes to 360 degrees. So how many degrees per minute?

anonymous · Answer

6 degrees per minute

anonymous · Answer

Right. And we're trying to figure out how many degrees there are for 20 minutes. $$\large \sf 20 \times 6 =120$$ so we're solving for 120 degrees. Do you know what 120 degrees looks like in radian form?

anonymous · Answer

ummmm 2pi/3

anonymous · Answer

Right. So part 1 done. Next it to find the distance the tip traveled. For this we'll use the formula $$\large \sf Arc~=~r \times \theta$$

anonymous · Answer

lol i dont get his part sry

anonymous · Answer

Well wanna use a different formula? We're looking for the distance the tip traveled. In other words, the arc it traveled around the circumference of the clock. |dw:1436398679715:dw|

anonymous · Answer

yes ok

anonymous · Answer

And we'll use the formula $$\large \sf Arc~=~r \times \theta$$ to find the arc length.

anonymous · Answer

This is the radian style formula by the way

anonymous · Answer

wait whats the unknowns

anonymous · Answer

So $\large \sf \theta=\frac{2\pi}{3}$

anonymous · Answer

yes is r=4?

anonymous · Answer

And r is stated in the top part of your question. Yeah, r is 4

anonymous · Answer

ok so theta= 4pi?

anonymous · Answer

$$\large \sf \theta=\frac{2\pi}{3}$$

anonymous · Answer

i mean arc sorry

anonymous · Answer

$$\large \sf Arc~=~4 \times \frac{2\pi}{3}$$$$\large \sf Arc~=~\frac{8\pi}{3}$$

anonymous · Answer

oh yea sry i multiplied wrong

anonymous · Answer

Anyways, Part 3 uses the same formula. The only difference is what we're solving for. $$\large \sf 3\pi~=~4 \times \theta$$