The Pythagorean Identity for CosineDate: 11/11/95 at 3:24:33 From: Mustafa KARA Subject: Hello from Turkey Dear sir, First of all, I want to say to you Thank You for helping me to solve my math problems. My question is this. If Sin 9 = x , what is the solution and result of Cos9.cos18.cos36? Thank you very much. Good bye. Mustafa Kara Date: 11/12/95 at 14:15:51 From: Doctor Ken Subject: Re: Hello from Turkey Hello! The main things you'll have to know to do this problem are the formula Sin[t]^2 + Cos[t]^2 = 1, and the formulas for Cos[2t] and Sin[2t]. For instance, where you have Cos[9], you want to write that in terms of Sin[9], so solve the "Pythagorean" identity for Cos[t]: Cos[t] = Sqrt{1 - Sin[t]^2}. So that means Cos[9] = Sqrt{1 - x^2}, right? So you can put that in the first part of your expression, and then you have: Cos[9]*Cos[18]*Cos[36] = Sqrt{1 - x^2}*Cos[18]*Cos[36]. You can kind of keep going in this fashion until you get something that's all in terms of x. Good luck! -Doctor Ken, The Geometry Forum |
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