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XM8 · Mar 30, 2009, 12:15 PM

Hi,

I'm having a spot of trouble.

I'm trying to do an exercise (cus I have a maths test tomorrow) and I can't figure this out.

A = cos (PI/3) - cos(2 PI/3) - cos (4 PI/3) + cos (5 PI/3) = 2

Why would that equal two? And what am I supposed to be subtracting and adding here? Value such as cos (pi/3) : 1/2 ?

Please help thanks

-Xm8

cdedmundson · Mar 30, 2009, 12:35 PM

you have the right idea. Cosine is a periodic function so it fluctuates between 1 and -1. it has a period of 2pi, meaning it completes one cycle over a domain of 2pi. So at x=o cos(x)=1, and x=pi cos(x)=-1, and x=pi/3 cos(x)=1/2, just add the four values and they add up to 2
(1/2)-(-1/2)-(-1/2)+(1/2)=2

XM8 · Mar 30, 2009, 01:06 PM

Hey cdEdmundson,

Thank you for your answer. I understand perfectly what you're saying it's just that I have a small problem and it would be great if you could help me with this.

Ok I know that the cosine of 2pi/3 is -1/2 as you mentioned above, and that it measures 120 degrees.

I use a trick my teacher gave me to find the location of any value on the unit circle.

Let's say he were to give me 97pi/3. What I would do is
96pi/3 + pi/3 = 32pi + pi/3 and I know that I would have to place the original value, 97pi/3 on the location of pi/3.

However, how would I decompose, or simplify 2pi/3 or 4pi/3 or even 3pi/3 ?

Thanks a lot,

-Xm8

Perito · Mar 30, 2009, 01:23 PM

Originally Posted by XM8

I know that the cosine of 2pi/3 is -1/2 as you mentioned above, and that it measures 120 degrees.

I use a trick my teacher gave me to find the location of any value on the unit circle.

Let's say he were to give me 97pi/3. What I would do is
96pi/3 + pi/3 = 32pi + pi/3 and I know that I would have to place the original value, 97pi/3 on the location of pi/3.

However, how would I decompose, or simplify 2pi/3 or 4pi/3 or even 3pi/3 ?

I subtract 2pi from every value, and repeat until I obtain a number less than 2pi. I then realize that pi radians is 180 degrees. 2pi/3 is simply

$\frac{2 * 180}{3}=120$

4pi/3 = $\frac{4 * 180}{3}=240$

3pi/3 = $\frac{3 * 180}{3}=180$

XM8 · Mar 30, 2009, 01:33 PM

Thanks Edmundson,

I know how to do that with small values it's just that if I get a big number I can't do the mulitply by 2pi thing because a) I won't have the time to figure it out b) I won't have a calculator and c) The result will be too big

That's why I try to figure out that rule my teacher gave me because there's always some kind of trick to it.. Hmm... I just don't get it.

Do you know of any other tricks?

Thanks,

-Xm8