1. ## possible to factor??

I used half angle formula to get from sin (x/2) + cos x = 0 -->
2cos^2 x - cos x + 1 = 0, but is it possible to factor?

I graphed the original on my calculator and the answer appears to be x=pi, but I want to understand how to arrive at that answer. I also want to arrive at that answer using the tools I have covered in the class, which at this point means using the half angle formula and trig id's. I have worked out cos (x/2) - sin x = 0 with no problem as I can factor it after using 1/2 angle formula.

2. Have you NEVER heard of the Quadratic Formula?

$\sqrt{(-1)^{2}-4(2)(1)} = \sqrt{1 - 8} = \sqrt{-7}$

Now what do you think about factoring?

You studied algebra BEFORE trigonometry for a reason. Do not forget your algebra. You will need it.

How sure are you that you used the half-ange identity correctly? With that square root in there, are you certain something didn't go wrong?

You may wish to check out $-\frac{\pi}{3}$ as well.

3. Hello, dashreeve!

I used half-angle formula to get from:

. . sin(½x) + cos(x) .= .0 . . 2cos²(x) - cos(x) + 1 .= .0 . . . . Wrong!

Use the identity: . cosθ .= .1 - 2sin²(½θ)

We have: .sin(½x) + 1 - 2sin²(½x) .= .0 . . 2sin²(½x) - sin(½x) - 1 .= .0

. . which factors: .[sin(½x) - 1] [2sin(½x) + 1] .= .0

Got it?