Question

How many radians on the unit circle would the minute hand travel from 0° if it were to move 3π inches?
What is the coordinate point associated with this radian measure?

Answer 1

@satellite73 @Loser66

Answer 2

I'm not sure if this is needed but here it is,

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.

Answer 3

@rational

Answer 4

Is the length of minute hand 4 in ?

Answer 5

Yes

Answer 6

The length travelled on "unit circle" equals the angle in radian measure. So simply find the angle intercepted in travelling 3pi inches on the clock

Answer 7

\[l=r\theta\]
plugin \(l=3\pi\), \(r=4\) and solve \(\theta\)

Answer 8

is it just \[\frac{ 3\pi }{ 4 }\]

Answer 9

Yep thats the angle in radians
also, thats the distance travelled on unit circle

Answer 10

that doesn't make sense
could you show it in more steps

Answer 11

do you mean

l = r(theta)
3pi = 4(theta)
3pi / 4 = theta

?

Answer 12

if so, looks good.

Answer 13

yes haha

Answer 14

just so you know, it is important to show the steps correctly.
there is no way for others to predict what you think/assume

Answer 15

ok, what about the second part of the question for coordinate plane?

Answer 16

coordinate point

Answer 17

A point has two coordinates : x, y

Answer 18

you can find them using :

\(x = r\cos(\theta)\)
\(y=r\sin(\theta)\)

Answer 19

\(r\) = radius of clock = \(4\)
\(y\) = angle from 0 degrees = \(\frac{3\pi}{4}\)

plug them

Answer 20

just \[4\cos (\theta)\]
?

Answer 21

\(x = r\cos(\theta) = 4*\cos(\frac{3\pi}{4}) = ?\)

Answer 22

i get \[\sqrt[-2]{2}\]
what does that simplify into?

Answer 23

you should be getting \(\large x = -2*\sqrt{2}\)

Answer 24

and \(\large y = 2*\sqrt{2}\)

so the required coordinate point would be
\[\large (-2\sqrt{2},~2\sqrt{2})\]

Answer 25

okay thank you, that's a weird coordinate,

Answer 26

np:)

Answer 27

btw, \(\sqrt{2}\) is just a number