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# Find The Exact Value

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Angle x is a third quadrant angle such that cos x = −2/3 .

What is the exact value of cos ( x / 2 ) ?

cos ( x / 2) =

I'm not 100% sure how to do this. I've seen problems similar to this, but I still have a hard time understanding. If someone could explain, I'd appreciate that lots!

Mar 30, 2020

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I haven't learned Algebra II yet, but I can provide you with a resource.

Mar 30, 2020
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I'm in Pre-calculus Trigonometry. I have to say, this is definitely the hardest time I've ever had with any math. This lesson is really hard. Most of it looks like a completely different language. I will definitely check out the resource you gave me, thank you so much:)

Mar 30, 2020
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I'm only in eighth grade. Is highschool hard? I'm going to highschool next year, I'm kind of scared!

AnExtremelyLongName  Mar 30, 2020
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Well, it depends on what your next math level is. I'm a senior! Mine was Algebra 1, Geometry, Algebra 2, & then Pre calc trig. Algebra was a breeze, and Geometry had it's moments, because my teacher wasn't great at explaining things, but I eventually got the hang of it.

I started online school this year, so it's been a lot harder for me to understand without an actual teacher, you know? I tend to catch onto things easily involving patterns, but Pre calc trig is ANYTHING but patterns. Seriously though, you just have to be patient. Math takes a lot of time. :) I'm sure you'll do great next year!

auxiarc  Mar 30, 2020
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NOOOOOOOO mine is Algebra II/Trig, Pre-calc, AP Calc, and calculus III !!! Life will be hard....

AnExtremelyLongName  Mar 30, 2020
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Let's hope we are in the same class next year

AELN, or should I say $$\text{very bad word that is so bad that it must be censored in LaTeX format}$$

CalculatorUser  Mar 30, 2020
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Yes, I hope so too! . CU, or should I say $$\text{biggest of the baddest of the badder of the bad word}$$?

AnExtremelyLongName  Mar 30, 2020
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Mar 30, 2020
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The video explains in angles of a triangle, but the question tells about the exact value being in the 3rd quadrant. I don't know if I'm missing something, but I don't think that the video will help me. Thank you though

auxiarc  Mar 30, 2020
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Mar 30, 2020
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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 .

Mar 30, 2020
edited by DragonLord  Mar 30, 2020
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Nice, Dragon!

AnExtremelyLongName  Mar 30, 2020
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Omigosh! Thank you so so so much!! I got sqrt of 6 over 6. Hopefully I'm right. :) Thank you again!!

auxiarc  Mar 30, 2020
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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!

Mar 30, 2020
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Nice! How are you able to take 5 grades above your level? Is it online classes or something? I should try that.

AnExtremelyLongName  Mar 30, 2020
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AELN, I like math a lot. It's my passion. I guess that's why

Mar 30, 2020
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I used to like math, then I discovered programming! Now I like that even more lol. I even convinced CU to do it.

AnExtremelyLongName  Mar 30, 2020
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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

Mar 30, 2020
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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.

Mar 30, 2020
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auxiarc, no problem, glad to help! :D

Mar 30, 2020