someone solve this trig identity prob for me too
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Originally Posted by magician,Apr 17 2006, 08:18 AM
Anyone who thinks that cos^2(x) means "cos square times x" clearly has no understanding of this material. "cos" by itself has no meaning; to think that you can multiply "cos" by "x" is absurd. While I could explain what it really means, you'd be better off studying your textbook and asking your professor.
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From: San Diego, Wess-Side!!
Originally Posted by gaus,Apr 16 2006, 09:03 PM
Here is the correct solution.
first use cos(x+y)=cosxcosy-sinxsiny.
cos(x+y)cos(x-y)=(cosxcosy-sinxsiny)(cosxcosy+sinxsiny)
=(cosxcosy)^2-(sinxsiny)^2 ; (use (a+b)(a-b)=a^2-b^2)
=cos^2xcos^2y-sin^2xsin^2y
=cos^2x(1-sin^2y)-(1-cos^2x)sin^2y
=cos^2x-cos^2xsin^2y-sin^2y+cos^2xsin^2y
=cos^2x-sin^2y.
first use cos(x+y)=cosxcosy-sinxsiny.
cos(x+y)cos(x-y)=(cosxcosy-sinxsiny)(cosxcosy+sinxsiny)
=(cosxcosy)^2-(sinxsiny)^2 ; (use (a+b)(a-b)=a^2-b^2)
=cos^2xcos^2y-sin^2xsin^2y
=cos^2x(1-sin^2y)-(1-cos^2x)sin^2y
=cos^2x-cos^2xsin^2y-sin^2y+cos^2xsin^2y
=cos^2x-sin^2y.
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From: Covington, LA
Believe it or not, this type of equation is used to determine stresses in 3D structural members. None of this is done by hand anymore, its all done with Finite Element Analysis software. But someone has to write the software and hence understand how to solve these types of equations. His course may make him solve a very simple set of equations like this in matrix form to show the concept and gain a better understanding of how the software works.
It is not untypical for the software to solve a matrix of equations that is represented by 1 million rows and by 1 million columns of equations like this simultaneously.
Knowing how to solve these types of equations has led to lighter, stronger, safer, and more efficient cars, buildings, space ships, cell phones, .........
So don't knock it just because you don't fully understand it.
It is not untypical for the software to solve a matrix of equations that is represented by 1 million rows and by 1 million columns of equations like this simultaneously.
Knowing how to solve these types of equations has led to lighter, stronger, safer, and more efficient cars, buildings, space ships, cell phones, .........
So don't knock it just because you don't fully understand it.
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Furthermore, even if you don't have to write finite-element software, having an understanding of the mathematics that underlies it can be useful in making rough estimates of the results. Why? Because it allows you to determine whether the output you get is reasonable or not. If not, it might suggest that you've made an error in your input specifications. You know: the type that leads to Mars landers to slam into the surface of the planet.
(I used DYNA2D and DYNA3D - two finite-element hydrocodes - in my work designing EFP warheads. Others in our office used NIKE2D and NIKE3D for analyzing designs of, for example, a fixture that had to spin one of the warheads to 300 RPS (18,000 RPM) before it was detonated. Cool stuff.
)
(I used DYNA2D and DYNA3D - two finite-element hydrocodes - in my work designing EFP warheads. Others in our office used NIKE2D and NIKE3D for analyzing designs of, for example, a fixture that had to spin one of the warheads to 300 RPS (18,000 RPM) before it was detonated. Cool stuff.
)
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