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#1 2006-11-27 03:38:35
- Kiran
- Member
- Registered: 2006-11-15
- Posts: 177
Help
solve the following equation if 0 <_ 0 < 2pi :
sin0 + 2sin^2 0 = 0
HELp
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#2 2006-11-27 05:05:06
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Help
I'm presuming by 0 you mean θ, because 0 isn't very good at being a variable.
So we have 2sin²θ + sinθ = 0.
This is a quadratic equation, and can be factorised into sinθ(2sinθ + 1) = 0.
Therefore, sinθ = 0 or -1/2.
Values of θ between 0 and 2π that make sinθ = 0 are 0 and π.
Values of θ between 0 and 2π that make sinθ = -1/2 are 7π/6 and 11π/6.
So your full answer is θ = 0, π, 7π/6, 11π/6.
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