So, I understand that the law of cosines is: $c^2 = a^2 + b^2 - 2\ a\ b \ cos(C)$
So how come, when calculating for an angle, the $-2\ a\ b$ becomes a positive divisor instead of staying negative?
i.e, why is it positive here: $\theta = arcos(\frac{a^2 \ +\ b^2 \ -\ c^2}{2\ a\ b})$
I'm confused because, am not dividing both sides by $-2 \ a \ b$ hence the second formula above to get the angle, it would remain a negative ($-2 \ a \ b$ ) instead of ($2 \ a \ b$ )?
What I am confused about is the exact process of how the sign changed to positive in the formula. nothing else.
$$c^2 = b^2 +a^2 - 2\ a\ b \ cos(\theta)$$ you can also write it as $$ 2\ a\ b \ cos(\theta) = b^2 + a^2-c^2 $$
thus $$ cos(\theta) = \frac{b^2 + a^2-c^2}{2 a b} $$ thus $$\theta = arcos(\frac{a^2 \ +\ b^2 \ -\ c^2}{2\ a\ b})$$