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 point 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 point associated with this radian measure?

zepdrix · Answer

So from 35 to 55 minutes, it moved 20 minutes, yes?
What portion of 60 minutes is this?
What? 1/3 you say? Yes very good!

Unlike degrees, radians is an actual measure. So we need to incorporate the radius.
The length of the minute hand is 4 inches.

So what we're really doing here is calculating 1/3 of the circumference of the clock.

zepdrix · Answer

They tell you to approach it with degrees first.
So maybe that would make more sense to you.

$$\Large\rm C=2\pi r$$
$$\Large\rm \frac{1}{3}C=\frac{2}{3}\pi r$$
Where $\Large\rm r=4~in$

Does that make sense?
It looks like they wanted you to approach it a little bit differently than I did: using degrees and then the arc length formula.

anonymous · Answer

yes thank you :)

zepdrix · Answer

Hmm I think part1 and part2 will be the same answer...
Maybe they're trying to trick us here... hmmmm

anonymous · Answer

Well...maybe you're right.

zepdrix · Answer

Well in part 2, they say how `far`...
so maybe they want your part2 in degrees.
I dunnooooo, grrrr!

Did you figure out part1? :o
Plugging in the 4 and stuff?

anonymous · Answer

uhhhhh lol this is totally hard

zepdrix · Answer

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zepdrix · Answer

Maybe I'm misreading part 1.
So it seems like maybe they just want to know how far the entire hand moves.
So we don't use the radius for part 1.

It's 20 minutes yes?
And a full rotation is 60 minutes?
So we traveled 1/3 of the full rotation.

What is that in radians?
Remember how much distance it is around in radians?
It's not 1 pie ;) because that would make too much sense, and math can be stupid sometimes.