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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-> 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.
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
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
Apply the Zero Product Rule:
or
Now recall the RANGE of the cosine function, i.e. . That means that is an extraneous root and can be discarded.
Hence, substituting back
The principal values of the argument for cosine are in the interval
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
