Question

Find the solutions of the equation that are in the interval [0, 2Ï€).
6 cos(^2) γ + 3 cos γ = 0

Answer 1

\[6 \cos ^{2}\beta + 3 \cos \beta = 0\]

Answer 2

Hey Liz :)
These terms have some stuff in common.
Let's factor that out and see what it looks like:\[\Large\rm 3\cos\beta(2\cos\beta+1)=0\]Yah

Answer 3

yah?

Answer 4

That's how far I got before I got stuck. I'm not sure where to proceed

Answer 5

Then we apply our `Zero-Factor Property`:\[\Large\rm 3\cos \beta=0,\qquad\qquad 2\cos\beta+1=0\]Setting each factor equal to zero,
and solve for beta in each case.

Answer 6

It's looks like your original question had gamma as the angle, not beta, but whatever hehe

Answer 7

@zepdrix
I got x = \[\pi/2 , 3\pi/2, 2\pi/3, 4\pi/3\] , but this is wrong...

Answer 8

From the first factor we get,\[\Large\rm 3\cos \beta=0\]\[\Large\rm \cos \beta = 0\]\[\Large\rm \beta=\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},~...\]But only the first two are within 2pi.
Ok good looks like you got those :)

Answer 9

From our other factor,\[\Large\rm 2\cos \beta+1=0\]\[\Large\rm \cos \beta = -\frac{1}{2}\]\[\Large\rm \beta=\frac{2\pi}{3},\frac{4\pi}{3},~...\]And your answer is wrong? 0_o hmmm thinking...

Answer 10

I think I just typed it in wrong! We got the right answers together! :)

Answer 11

oh yay \c:/
good job!