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MathGroup Archive 1995

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Re: Simple problem for math wiz

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1767] Re: [mg1685] Simple problem for math wiz
  • From: Allan Hayes <hay at haystack.demon.co.uk>
  • Date: Wed, 26 Jul 1995 00:53:46 -0400

REVEAL <nomail at me.net> in
[mg1685] Simple problem for math wiz
asks

> Anyone here know how to find the solution set to: sin^2x+sinx-1=0  
? > the trick, that is?
> (limited to trig & algebra)


Solve[Sin[x]^2 + Sin[x] - 1 == 0,x]
	Solve::ifun: Warning: Inverse functions are being used by 	
	Solve, so some solutions may not be found.
	
	              -1 - Sqrt[5]                 -1 + Sqrt[5]
	{{x -> ArcSin[------------]}, {x -> ArcSin[------------]}}
	                   2                            2


Although, as Porfirio Beltran observed in [mg1708],


Solve[Sin[x]^2 + Sin[x] - 1 == 0]
	            -1 - Sqrt[5]              -1 + Sqrt[5]
	{{Sin[x] -> ------------}, {Sin[x] -> ------------}}
	                 2                         2



For the copmplete solution you need to add multiples of 2Pi.

Allan Hayes
De Montfort University, Leicester
hay at haystack.demon.co.uk


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