- #1
TrueStar
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Homework Statement
Find all solutions to the equation in the interval [0,2[tex]\pi[/tex]] algebraically.
cos2x(2cos+1)=0
Homework Equations
NA
The Attempt at a Solution
This is what I've done, but I don't think it's right. I set cos2x=0 and 2cos+1=0. Since cos2x is a multi-angle, I let t=2x and rewrote it as cost=0 That means t equals [tex]\pi[/tex]\2+n[tex]\pi[/tex].
That also means 2x=[tex]\pi[/tex]\2+n[tex]\pi[/tex]. After dividing out the 2, I get x=[tex]\pi[/tex]\4+n[tex]\pi[/tex]\2.
I get the answers [tex]\pi[/tex]\4, 3[tex]\pi[/tex]\4, 5[tex]\pi[/tex]\4, and 7[tex]\pi[/tex]\4. This doesn't seem right to me. Shouldn't I only get two answers.
The other one seems easier. I got cosx by itself and it is cosx=-1\2. That means x is equal to 2[tex]\pi[/tex]\3 and 4[tex]\pi[/tex]\3.
Am I doing this correctly?
Thanks!