find the exact solution for

2cosx+1=0

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- Dec 2nd 2007, 08:51 AMcumanasolve equation
find the exact solution for

2cosx+1=0 - Dec 2nd 2007, 09:25 AMSoroban
Hello, cumana!

You must have*some*idea . . .

Quote:

Find the exact solution for: .$\displaystyle

2\cos x + 1\:=\:0$

What angle has a cosine of $\displaystyle \frac{1}{2}$ ?

You're expected to know that: .$\displaystyle \cos\frac{\pi}{3} \:=\:\frac{1}{2}$

Since cosine is negative in Quadrants 2 and 3,

. . the answers are: .$\displaystyle x \;=\;\frac{2\pi}{3},\:\frac{4\pi}{3}$

These are the answers in the interval $\displaystyle [0,\,2\pi]$

. .*You*can generalize them.

- Dec 2nd 2007, 09:28 AMTKHunny
If you REALLY have no idea how to approach that problem, my inclination is to assume that you have not paid attention in class for the last three years. Can it be?

2cos(x)+1=0

2cos(x) = -1

cos(x) = -1/2

$\displaystyle x\;=\;\frac{2\pi}{3}\;=\;2k\pi,\frac{4\pi}{3}\;+\; 2k\pi\;for\;\pi\;an\; Integer$

I'll just leave it at that. If you don't know what that means or how it happened, I'm going back to my original comments. Let's see where you are. Please have SOME idea. - Dec 2nd 2007, 09:40 AMcumana
okie, so i do have some idea, i just didnt know how to go about solving a problem like this one, and my book is rather vague :( thank you very much though