ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: lacoste on April 17, 2009, 01:39:43 pm

Title: unit circle
Post by: lacoste on April 17, 2009, 01:39:43 pm: would it useful to remember all of the values of a unit circle including the 2nd 3rd and 4th quadrant values?
Title: Re: unit circle
Post by: TrueTears on April 17, 2009, 01:40:26 pm: values as in....?

If you mean things like 2nd quadrant is $\pi - \theta$

3rd is $\pi + \theta$

4th is $2\pi - \theta$

They should be second nature to you by the time of the exam.
Title: Re: unit circle
Post by: Flaming_Arrow on April 17, 2009, 01:48:19 pm: i think he means the exact values

if you know what quadrants which 1 is positve and negative you should be fine

eg sin is positive in the 2nd quad

$\sin(\frac{3\pi}{4}) = \sin(\frac{\pi}{4}) =\frac{\sqrt{2}}{2}}$

cos is negative in the 2nd quad

$\cos(\frac{3\pi}{4}) =\frac{-\sqrt{2}}{2}}$
Title: Re: unit circle
Post by: TrueTears on April 17, 2009, 01:49:53 pm: Oh if you are talking about exact values, then you should be able to work them out systematically, by remember what the signs are in each quadrant and then using the quadrant 'rules'
Title: Re: unit circle
Post by: Flaming_Arrow on April 17, 2009, 01:50:27 pm: latex is failing again
Title: Re: unit circle
Post by: TrueTears on April 17, 2009, 01:51:23 pm: Quote from: Flaming_Arrow on April 17, 2009, 01:50:27 pm
latex is failing again
oh lol, i thought it was my computer that didn't refresh properly and couldn't see latex, so i refreshed like 50 times LOL
Title: Re: unit circle
Post by: EvangelionZeta on April 17, 2009, 03:48:16 pm: To answer the topic creator's question directly - yes, it is almost essential you remember exact values for all quadrants of the unit circle. The Methods exams love throwing questions involving them at you.
Title: Re: unit circle
Post by: NE2000 on April 17, 2009, 04:11:40 pm: And if in doubt, remember the isosceles and equilateral triangles that gave us these exact values in the first place.
Title: Re: unit circle
Post by: lacoste on April 17, 2009, 05:32:44 pm: What I mean is the entire unit circle of values.
Theres an attachment
Title: Re: unit circle
Post by: shinny on April 17, 2009, 05:39:45 pm: Like people have said, definitely memorise the exact angles for the first quadrant. As for the rest of the unit circle (2nd, 3rd, 4th quadrants), learn to derive those by applying symmetry to the first quadrant values.
Title: Re: unit circle
Post by: lacoste on April 17, 2009, 07:55:07 pm: Quote from: shinny on April 17, 2009, 05:39:45 pm
Like people have said, definitely memorise the exact angles for the first quadrant. As for the rest of the unit circle (2nd, 3rd, 4th quadrants), learn to derive those by applying symmetry to the first quadrant values.

Ahh okay. But is it handy to just memorise the other quadrants' exact values. For example, I think there was a question where you had to know what a quadrant a certain value was, and the only way I could work it out was to convert it to degrees and then work it out from there. I think it took way too long though. Is there a quicker way?

[hope you know what im talking about =/ ]
Title: Re: unit circle
Post by: shinny on April 17, 2009, 08:01:10 pm: Quote from: lacoste on April 17, 2009, 07:55:07 pm
Quote from: shinny on April 17, 2009, 05:39:45 pm
Like people have said, definitely memorise the exact angles for the first quadrant. As for the rest of the unit circle (2nd, 3rd, 4th quadrants), learn to derive those by applying symmetry to the first quadrant values.

Ahh okay. But is it handy to just memorise the other quadrants' exact values. For example, I think there was a question where you had to know what a quadrant a certain value was, and the only way I could work it out was to convert it to degrees and then work it out from there. I think it took way too long though. Is there a quicker way?

[hope you know what im talking about =/ ]

I wouldn't bother memorising the exact values for the other quadrants since that's just asking to make careless mistakes. Heck, someone I know who got 50 methods and spesh said himself that he doesn't memorise ANY of the exact values; rather, he derives them using the triangles previously mentioned on the spot, every time, as this prevents any chance of making careless mistakes, which can be very costly in VCE. Overall, just learn the symmetry rules for the other quadrants and you should be fine. As for that question, there would definitely have been a better way to do it. I'd need the question to see how though...
Title: Re: unit circle
Post by: lacoste on April 17, 2009, 08:30:52 pm: I can't remember the exact question as I don't have my computer with me.

But the concept is like this qst.

Find the exact value of sin(7pi/6)?

how would you know which quadrant it is in?

Thanks.
Title: Re: unit circle
Post by: Damo17 on April 17, 2009, 08:37:13 pm: Quote from: lacoste on April 17, 2009, 08:30:52 pm
I can't remember the exact question as I don't have my computer with me.

But the concept is like this qst.

Find the exact value of sin(7pi/6)?

how would you know which quadrant it is in?

Thanks.

$\frac{7\pi}{6}$ would be $\pi+ \frac{\pi}{6}$ so $sin\frac{7\pi}{6}$ would be in the 3rd quadrant. sin is negative in the 3rd so the exact value would be:
$<br />sin\frac{7\pi}{6}= -sin\frac{\pi}{6}$
$= -\frac{1}{2}$