Question

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⎯

Answer 1

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

Answer 2

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

Answer 3

it's the same as a reference angle

Answer 4

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

Answer 5

I believe so

Answer 6

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

Answer 7

zepdrix no I put that in it was incorrect :/

Answer 8

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.

Answer 9

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 \(\large\rm 4.5-\pi\).

Answer 10

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

Answer 11

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