SOLUTION: Use a calculator to find all solutions in the interval (0, 2π). Round the answers to two decimal places. (Enter your answers as a comma-separated list. If there is no solution
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Question 691290: Use a calculator to find all solutions in the interval (0, 2π). Round the answers to two decimal places. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
5 cos3 x − 20 cos2 x + cos x − 4 = 0
Hint: Factor by grouping. Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! (In the future please use "^" to indicate exponents. Otherwise it is impossible to tell the difference between and cos(3x). I was not going to even try this problem because I could not tell the difference. It is only the "factor by grouping" that helped me figure out that the 3 and the 2 must be exponents.)
Factoring by grouping...
Group the first two terms and the last two terms:
Factor out the Greatest Common Factor (GCF) of each group. (Note: This is one of the rare cases when one actually factors out a GCF of 1!)
As we can see we have a common factor between the two groups: cos(x) - 4. We can factor out this common factor:
From the Zero Product Property: or
Solving the first one...
At this point we should realize that there is no solution to this equation. Squaring a cos (or anything for that matter) cannot result in a negative number.
Solving the second equation:
Again we should recognize that there is no solution. A cos cannot be larger than 1!
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