DragonLord

Thank you! To both of you!

Ohh, I see! Thank you Melody!

I apologize for the misunderstanding, as I meant the length between the two points F_2 and F_1.

I would appreciate if you gave a solution following your statement. Thanks in advance.

Great work! Well done!

auxiarc, no problem, glad to help! :D

AELN, cool! I like programming as well. I took Java class before, it was pretty fun. Hmm...strange the range still doesn't work. Oh well, it's basically the range you can see multiplied by 2.

Arggh, for my solution, the LaTeX doesn't like when I input that range. It does that weird glitch thing. \

The range is (hopefully this works) \(0

AELN, I like math a lot. It's my passion. I guess that's why 

Thank you AELN. I wish Dragons were real...haha. I'm in 6th and take Algebra 2, and knows basic Pre-calc, :P. Not fully sure what the problem meant, but auxiarc should be able to get the hang of it!

Start by the identity \(\cos\left(\frac{x}{2}\right)=\pm\sqrt{\frac{1+\cos x}{2}}\) 

I'm assuming the range of \(x\) in this problem is in the range of \(0  (Sorry if this is the wrong range, I assumed this range because for problems normally like this thats the range they use.)

Notice that this range can also be \(0<\frac{x}{2}<\frac{\pi}{4}.\) 

Since \(\cos\) is positive here, we use \(\sqrt{\frac{1+\cos x}{2}}\)

Since \(x=-\frac{2}{3}\) , then \(\sqrt{\frac{1-2/3}{2}}.\)

I will leave the radical simplification to you. If you need further help, contact me .

When I post a problem, I will enter the problem with numbers, and below it, show my work process. Then, they know where I've gotten and that at least I tried. You posted this problem carelessly, without numbers because of LaTeX, and does not include any of your work. Did I directly beg for answers from a certain person? No. If someone answers my problem I always thank them and read their explanations thoroughly, until I understand the problem. Then, I completely redo the problem trying not to look at their explanations, so I can grasp the meaning. Furthermore, you are directly asking for certain people to answer your problems. That's basically stating that one person is better than another. If you haven't noticed, I box my answers to make things neat and look better, not to feed people answers. I also give them an explanation, and if they don't read my explanations, I can't stop them. This ends here. That is final.