SOLUTION: solve {{{2 cos^2(x) - 5cos(x) + 2 = 0}}} for all principal values of x.
I am not sure where nor how to proceed with problem. Am I supposed to use a Pythagorean identity, and if
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Question 596831: solve for all principal values of x.
I am not sure where nor how to proceed with problem. Am I supposed to use a Pythagorean identity, and if so, where do I go from there. Any help you can give me would be so greatly appreciated. I am struggling through my precalculus book, and I did not do well in Trig or Geometry and passes Algebra I and II with a mid C. Please help me understand this problem.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First of all, I fixed your equation. )
means the cosine of the angle 
, whereas )
is the squared value of the cosine function at 
. Very different things and they didn't give you
\ -\ 5\cos(x)\ +\ 2\ =\ 0)
in a Precalculus book.
The easiest way to see what is going on in this equation is to use a simple substitution.
Let )
and substitute.
Factor the quadratic in 
(u\ -\ 2)\ =\ 0)
Apply the Zero Product Rule:
or
Now recall the RANGE of the cosine function, i.e. \ \leq\ 1)
. That means that 
is an extraneous root and can be discarded.
Hence, substituting back
\ =\ \frac{1}{2})
The principal values of the argument for cosine are in the interval
\ \leq\ \pi)
Find the two angles in the unit circle where the -coordinate is equal to 
and select the one that is in the principal value interval.
John
My calculator said it, I believe it, that settles it
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