Question

Trigonometry help?

Answer 1

what is your question?

Answer 2

Any help is appreciated

Answer 3

Great, I don't give answers just explanations :) Nice to meet you

Answer 4

Nice to meet you too :)

Answer 5

there are 60 minutes on the dial
there are 360 degrees per circle

so.... how many degreee is 1 minute?

Answer 6

6?

Answer 7

yes

Answer 8

\(\bf \cfrac{360d}{60m}\implies 6\frac{d}{m}
\\ \quad \\
radians =\cfrac{degrees\cdot \pi}{180}\implies \cfrac{6\cdot \pi}{180}\implies \cfrac{\pi}{30}\)

Answer 9

so... from 3:35 to 3:55 it went 20mins
or 20 * that much in radians

Answer 10

120 degrees=2pi/3 radians. Correct?

Answer 11

yes

Answer 12

\(\bf 20\cdot \cfrac{\pi}{30}\implies \cfrac{\cancel{20}\pi}{\cancel{30}}\implies \cfrac{2\pi}{3}\)

Answer 13

Ok so part one is solved. For part 2 how do I determine how far the tip of the minute hand travels between 3:35 and 3:55?

Answer 14

how far does the tip go? or.... what' the "arc" it makes?

well, we know the hand minute is 6inches long and the angle it makes is \(\bf \cfrac{2\pi}{3}\) so \(\bf \textit{arc length}= s = r\theta\implies 6\cdot \cfrac{2\pi}{3}\)

Answer 15

4pi?

Answer 16

yes

Answer 17

Give me a few minutes. I'm trying to see if I can get parts 3 and 4 on my own

Answer 18

part 3 is more or less a given really

Answer 19

I have no idea what to do

Answer 20

hmm ... lemme see

Answer 21

Ok

Answer 22

I see the arc is \(3\pi\) long... ok

so we know the minute tip moved form 0 to \(3\pi\) position, that is the arc moved that much along

we know the radius is the same, 6 inches, the hand is not getting any longer =)

so keep in mind that if the minute hand moved from 0 position to \(3\pi\) later
it made an arc that is \(3\pi\) long thus \(\bf \textit{arc length}= s = r\theta\qquad s=3\pi\qquad r=6
\\ \quad \\
3\pi = 6\cdot \theta\implies \cfrac{3\pi}{6}=\theta\)

Answer 23

I went back to part 2 to convert it to degrees is 4pi radians really 720 degrees?

Answer 24

yeap, keep in mind that \(\bf 360^o=2\pi\implies 360^o\cdot 2\implies 2\pi\cdot 2\)

Answer 25

How can the tip of the minute hand travel 720 degrees in 20 minutes?

Answer 26

haemm it doesn't

Answer 27

ohhh wait... I see .... your issue

Answer 28

the issue is
the exercise is using radians for the angle made by the hand
and ALSO using radians for the length of the arc it makes on the circle

Answer 29

and yes, most of the time, you'd use radians mostly for angles, though they're not restricted to that only

Answer 30

So the answer is still correct?

Answer 31

\(\bf \textit{arc length}= s = r\theta\implies 6\cdot \cfrac{2\pi}{3}\implies 4\pi \approx 12.57\ inches\)

Answer 32

the arc is measured in inches, since that's what we have for the length unit of the hand

Answer 33

Ooooh, I see

Answer 34

How would I find the coordinate point?

Answer 35

lemme recheck stuff =)

Answer 36

Ok no problem

Answer 37

anyhow...the values are correct... well.... how to get 4

Answer 38

I'm not sure how to find a coordinate point on a unit circle

Answer 39

the coordinates, that is the "x" and "y" for any point on the circle with an angle \(\theta\) are always at \(\bf [cos(\theta)\quad , \quad sin(\theta)]\)

Answer 40

so.... \(\bf \textit{arc length}= s = r\theta\qquad s=3\pi\qquad r=6
\\ \quad \\
3\pi = 6\cdot \theta\implies \cfrac{3\pi}{6}=\theta\iff \cfrac{\pi}{3}\quad at \quad \left[cos\left(\frac{\pi}{3}\right)\quad ,\quad sin\left(\frac{\pi}{3}\right)\right]\)

Answer 41

I'd think your Unit Circle would have those values anyway, that's a pretty well known angle

Answer 42

Isn't it 3pi/6 simplified as pi/2?

Answer 43

ohh shoot... yes, just notice that =)

Answer 44

\(\bf \textit{arc length}= s = r\theta\qquad s=3\pi\qquad r=6
\\ \quad \\
3\pi = 6\cdot \theta\implies \cfrac{3\pi}{6}=\theta\iff \cfrac{\pi}{2}\quad at \quad \left[cos\left(\frac{\pi}{2}\right)\quad ,\quad sin\left(\frac{\pi}{2}\right)\right]\)

Answer 45

Ok awesome. You were a TREMENDOUS help. I'm giving you best response right now

Answer 46

yw