# Thread: X-Coordinates on Tangent Line

1. Originally Posted by Jhevon
are you taking me for a ride? or are you really trying? *suspicious smiley (we still need one of these)*

$2 \cos^2 x - \cos x - 1 = 0$ ....this is a quadratic, see if you can factorize

$\Rightarrow (2 \cos x + 1)(\cos x - 1) = 0$

$\Rightarrow 2 \cos x + 1 = 0 \mbox{ or } \cos x - 1 = 0$

$\Rightarrow \cos x = - \frac 12 \mbox{ or } \cos x = 1$

what angles does this happen for?
45 degree angles? and I'm trying to the best of my memory. Sorry if I'm wasting your time

2. Originally Posted by FalconPUNCH!
45 degree angles? and I'm trying to the best of my memory. Sorry if I'm wasting your time
you are only wasting my time if you're letting me do your homework for you, otherwise, if you're actually trying (and learning) i am more than happy to help.

there are two things you must consider:

$\cos x = - \frac 12$

and

$\cos x = 1$

$x = 45^o$ is not a solution to either of those equations. and by the way, we think of angles to be in radians when doing calculus, unless otherwise stated.

think of the graph of cosine, think of the special angles and think of the quadrants in which the reference angles of the special angles appear and try again

3. I give up I'm just going to ask the teacher tomorrow for help. Sorry I have a lot of other problems that I should be doing right now but I'm wasting my time with this one.

4. Originally Posted by FalconPUNCH!
I give up I'm just going to ask the teacher tomorrow for help. Sorry I have a lot of other problems that I should be doing right now but I'm wasting my time with this one.
$\cos x = - \frac 12$

$\Rightarrow x = \frac {2 \pi}3 + 2 n \pi$ for $n \in \mathbb{Z}$ or $x = \frac {4 \pi}3 + 2n \pi$ for $n \in \mathbb{Z}$

$\cos x = 1$

$\Rightarrow x = 2n \pi$ for $n \in \mathbb{Z}$

now choose the angles that fall into the region you want

5. Originally Posted by Jhevon
$\cos x = - \frac 12$

$\Rightarrow x = \frac {2 \pi}3 + 2 n \pi$ for $n \in \mathbb{Z}$ or $x = \frac {4 \pi}3 + 2n \pi$ for $n \in \mathbb{Z}$

$\cos x = 1$

$\Rightarrow x = 2n \pi$ for $n \in \mathbb{Z}$

now choose the angles that fall into the region you want
Thanks for your I'll finish it later. You didn't have to do that I'm just trying to figure out how to do implicit differentiations right now.

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