SOLUTION: Hi, Solve cosx-3sinx=3. I get -1/2 and -1. Am I correct? Thank you.

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, Solve cosx-3sinx=3. I get -1/2 and -1. Am I correct? Thank you.      Log On


   

Question 1202972: Hi,
Solve cosx-3sinx=3.
I get -1/2 and -1.
Am I correct?
Thank you.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve cosx-3sinx=3.
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cos(x)-3sin(x) = 3
cos(x) = 3sin(x) + 3
cos^2(x) = 9sin^2(x) + 18sin(x) + 9
1 - sin^2(x) = 9sin^2(x) + 18sin(x) + 9
10sin^2(x) + 18sin(x) + 8 = 0
5sin^2(x) + 9sin(x) + 4 = 0
(5sin + 4)*(sin + 1) = 0
sin(x) = -1 --> x = 3pi/2 + n*2pi, n = integer
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sin(x) = -4/5 --> x =~ 5.356 + n*2pi, n = integer
x in radians.