anonymous
  • anonymous
Medal award! Suppose you start at the point (1,0) on a unit circle and move a distance t = 4.5 along the circle. What is the reference number for t? Give an exact answer. Your answer may have pi in it! Please PREVIEW! The reference number for 4.5 is t⎯
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
i have no idea what a "reference number" is , do you know?
anonymous
  • anonymous
i have a guess, my guess is \(2\pi-4.5\) but that is really just a guess
anonymous
  • anonymous
it's the same as a reference angle

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anonymous
  • anonymous
oh, that kind of begs the question is a "reference angle" between \(0\) and\(\frac{\pi}{2}\)?
anonymous
  • anonymous
I believe so
zepdrix
  • zepdrix
Hmm ya the wording is a little strange here :d So we're starting at pi/2, ya? We're spinning 4.5 around,\[\large\rm \frac{\pi}{2}+4.5\]The way we get back to the reference angle depends on which quadrant we lie in. Turns out we're in quadrant 4, so to get our reference angle we would do \(\large\rm 2\pi-\theta\) So I guess we haveeeeee\[\large\rm 2\pi-\left(\frac{\pi}{2}+4.5\right)\]That seems kinda complicated though >.< Maybe that's not what they wanted hmm
anonymous
  • anonymous
zepdrix no I put that in it was incorrect :/
zepdrix
  • zepdrix
Oh I'm so silly. We're starting at (1,0), not at (0,1)... So we're starting at an angle of 0, not pi/2.
zepdrix
  • zepdrix
Spinning to 4.5 puts us at \(\large\rm 0+4.5\) which is in quadrant 3. So to get back to our reference angle we would do \(\large\rm 4.5-\pi\).
anonymous
  • anonymous
thanks so much :) may I ask how you got 4.5?
zepdrix
  • zepdrix
|dw:1444007447856:dw|Here is a handy chart showing you how to get your reference angle from each quadrant.
zepdrix
  • zepdrix
|dw:1444007656117:dw|So we started here at (1,0).
zepdrix
  • zepdrix
|dw:1444007714494:dw|If we pi radians around the circle, we'd be going approximately 3.14 around.
zepdrix
  • zepdrix
|dw:1444007764708:dw|But they told us to go 4.5 around. So we have to go further. To figure out which quadrant you should be in, you need the decimal value for 3pi/2.
zepdrix
  • zepdrix
3pi/2 ends up being approximately 4.7 4.5 is smaller than that value, so we're in quadrant 3! :)
zepdrix
  • zepdrix
And if you look back at my original chart, it shows you how to get from quad 3 to reference angle.
anonymous
  • anonymous
ok :) thanks so much.. it's actually 3.5 not 4.5 though
zepdrix
  • zepdrix
what? 0_o it says 4.5 twice in the problem though lol
anonymous
  • anonymous
I have one that I was working on that's exactly the same for practice :) Thanks so much
zepdrix
  • zepdrix
oh cool :3

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