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December 22, 2014

December 22, 2014

Posted by **Devon** on Monday, April 16, 2007 at 9:57pm.

cos^2x=3-5cosx

Devon, what grade level are these questions from?

I am having the same problems as with your 9:14 post.

Please see my partial solution in the post to bobpursely at 10:54

Devon, I have been misreading your questions, yes, they are readily solvable.

cos^2(x) + cosx -3 = 0, treat it as a quadratic with cosx the variable

I got cosx = .54138 or cosx = -5.5...

The last one is not possible so we have to use

cosx = .54138

using arccos gives us 57.2º

Now recall that the cosine in positive in the first and fourth quadrants, so

x=57.2º or 360º-57.2º = 302.8º

these answers are in the domain 0<x<360, if you want a general answer it would be

x = 57.2 + 360n or 302.8 +360n where n is an integer.

For radians, set your calculator to RAD and follow the above method

For general solutions add 2(pi)n to each answer you found

thank you so much, i totally understand it now!

to your grade level question, i'm in 9th grade, but i'm pretty sure it's 11th grade material.

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