# General solution using reciprocal identities

• Nov 25th 2012, 08:44 AM
Twinkie
General solution using reciprocal identities
Ok, I can't figure out how to do this. I understand that you treat this like X^(2)+ X+1 and I can get to the point where you find what cos is equil to, but when puting the unit circle vallues is where im confused. Ok I have recently swiched to schools because I just had surgery so I couldnt be around that many people at a time. My other teacher told us we could not have decimal answers in this unit and in this new book I got there is decimal answers in it. I have no idea how to get the decimal answers. So here is the question Im trying to figure out.

Solve the equation algibraically over the domain 0<X<2pie: sec^(2)X + 5secX+ 6=0

This is my work, please tell me if im doing anything wrong
(sec+3)(sec+2)=0
secX=-3 secX=-2
1/(cos -3) 1/(cos -2)
cos= -1/3 cos=-1/2

2pie/3, 4pie/3...
So, now how do I get the decimal answers?
The book say the answers are 4pie/3, 2pie/3, 4.37, 1.91
• Nov 25th 2012, 09:00 AM
skeeter
Re: General solution using reciprocal identities
$\displaystyle \cos{x} = -\frac{1}{2}$ is a unit circle value ... $\displaystyle x = \frac{2\pi}{3}$ , $\displaystyle x = \frac{4\pi}{3}$

$\displaystyle \cos{x} = -\frac{1}{3}$ has two solutions, one in quad II and one in quad III

$\displaystyle x = \arccos\left(-\frac{1}{3}\right)$ gives the solution in quad II

$\displaystyle x = 2\pi - \arccos\left(-\frac{1}{3}\right)$ gives the quad III solution

btw, this is pi ...

http://4.bp.blogspot.com/_PNe-bgIDyR...ig/s200/pi.png

and this is pie ...