Posted by Anonymous on Thursday, January 3, 2013 at 5:14pm.
Please help!!!!!!!!!!! Find all solutions to the equation in the interval [0,2π).
Solve algebraically for exact solutions in the interval [0,2π). Use your grapher only to support your algebraic work.
- Precalculus - bobpursley, Thursday, January 3, 2013 at 5:40pm
Have you tried the double angle formulas?
- Precalculus - Anonymous , Thursday, January 3, 2013 at 5:58pm
Yes. It is just too hard and it would be nice if you would just explain it to me or show me an example. Please.
- Precalculus - bobpursley, Thursday, January 3, 2013 at 6:07pm
Hard? Why would anyone want to do something easy?
2cos^2x+cosx=cosx= cos(x)cos(x) - sin(x)sin(x) = cos²(x) - sin²(x)
2 cos^2 x+cosx=cos^2x-(1-cos^2x)
2 cos^2 x+cosx=2cos^2x-1
- Precalculus - Steve, Thursday, January 3, 2013 at 6:44pm
the only way to make these easy is to do dozens of them, not just the assignments. The double angle formulas are critical to know.
cos 2x + sin x=0
1 - 2sin^2 x + sin x = 0
rearrange things a bit to the usual order:
2sin^2 x - sin x - 1 = 0
(2sin x + 1)(sin x - 1) = 0
so, either sin x = -1/2 or sin x = 1
sin x = -1/2: x = 7pi/6 or 11pi/6
sin x = 1: x = pi/2
- Precalculus - Anonymous , Thursday, January 3, 2013 at 9:33pm
Thanks for your help you guys.
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