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Pianoman1996j
 2 years ago
How do you solve
\[\cos 2 x= cos x +2\]
Pianoman1996j
 2 years ago
How do you solve \[\cos 2 x= cos x +2\]

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phi
 2 years ago
Best ResponseYou've already chosen the best response.1do you know cos(x+y) formula?

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1Yes cosxcosy+sinxsiny

phi
 2 years ago
Best ResponseYou've already chosen the best response.1almost, the add turns into a minus (it's ugly that way) if you use that with y= x cos(x+x)= cos^2 x  sin^2 x replace sin^2 with 1cos^2 : cos^2  1  cos^2 or 2cos^2(x) 1

phi
 2 years ago
Best ResponseYou've already chosen the best response.1you can replace the cos(2x) with 2 cos^2(x) 1 if you call cos(x) y you have 2y^2 1 = y+2 solve for y

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1I think. I will spend some time with it now. Thanks.

phi
 2 years ago
Best ResponseYou've already chosen the best response.1of course, after you find y, you find x using x = inverse cos(y) because this is a quadratic, you will get two answers for y then we have to figure out the the answers for every 2pi

phi
 2 years ago
Best ResponseYou've already chosen the best response.1*typo replace sin^2 with 1cos^2 : cos^2  (1  cos^2)= cos^2 1 + cos^2 or 2cos^2(x) 1

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1I think I have it! Hang on while I try to finish!!

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1I got y=3/2 and y=1. So 1 is at pi but what about 3/2. My teacher says pi is the only answer? Why?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1the cosine goes between 1 and +1 (it never goes outside that range) . There is no angle whose cos is > 1 so you can't get 3/2

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1Of course! Thanks for helping me see.

phi
 2 years ago
Best ResponseYou've already chosen the best response.1and because the cosine repeats, you can add any multiple of 2pi to your answer and it will work. to be complete the answer is \[ \pi + 2\pi n \]where n is any integer

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1Is there any trick to knowing which formula to try? I often grab one that would be allowed but isn't the one I should have used.

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1I only had to give solutions between 0 and 2pi but I like your further explaination

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1Oops. Explanation I mean

phi
 2 years ago
Best ResponseYou've already chosen the best response.1Unfortunately, with trig I think you just have to do a bunch of problems and build a sense of what might work.

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1Lol. I've done hundreds and am still picking the wrong ones. But I'm not giving up yet!

Pianoman1996j
 2 years ago
Best ResponseYou've already chosen the best response.1Thanks for help. my midterm is soon. Yikes.
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