## anonymous one year ago 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⎯

1. anonymous

i have no idea what a "reference number" is , do you know?

2. anonymous

i have a guess, my guess is $$2\pi-4.5$$ but that is really just a guess

3. anonymous

it's the same as a reference angle

4. anonymous

oh, that kind of begs the question is a "reference angle" between $$0$$ and$$\frac{\pi}{2}$$?

5. anonymous

I believe so

6. 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

7. anonymous

zepdrix no I put that in it was incorrect :/

8. 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.

9. 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 $$\large\rm 4.5-\pi$$.

10. anonymous

thanks so much :) may I ask how you got 4.5?

11. zepdrix

|dw:1444007447856:dw|Here is a handy chart showing you how to get your reference angle from each quadrant.

12. zepdrix

|dw:1444007656117:dw|So we started here at (1,0).

13. zepdrix

|dw:1444007714494:dw|If we pi radians around the circle, we'd be going approximately 3.14 around.

14. 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.

15. zepdrix

3pi/2 ends up being approximately 4.7 4.5 is smaller than that value, so we're in quadrant 3! :)

16. zepdrix

And if you look back at my original chart, it shows you how to get from quad 3 to reference angle.

17. anonymous

ok :) thanks so much.. it's actually 3.5 not 4.5 though

18. zepdrix

what? 0_o it says 4.5 twice in the problem though lol

19. anonymous

I have one that I was working on that's exactly the same for practice :) Thanks so much

20. zepdrix

oh cool :3