SOLUTION: The solutions of cos2x – cos x – 2 = 0 are (where k denotes an arbitrary integer)
I know the answer is −π + 2kπ, I just have no idea how to get to that point.
Algebra ->
Trigonometry-basics
-> SOLUTION: The solutions of cos2x – cos x – 2 = 0 are (where k denotes an arbitrary integer)
I know the answer is −π + 2kπ, I just have no idea how to get to that point.
Log On
Question 384531: The solutions of cos2x – cos x – 2 = 0 are (where k denotes an arbitrary integer)
I know the answer is −π + 2kπ, I just have no idea how to get to that point. Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! If you let z = cos x, then the equation becomes a simple quadratic:
(I hope the cos2x means , otherwise we'd need the power reduction formulas).
From the quadratic, we can factor and obtain --> z = 2 or z = -1. However, z is only defined on [-1, 1] since it is the range of cosine, so z = -1, and x = -pi (plus any multiple of 2pi since they denote the same angle on a unit circle).
