Math Is Fun Forum

Pixel

Member

Registered: 2009-11-25

Posts: 2

Help!!!

There's no answer for this in the back of the book and I just want to make sure I did it correctly. If anyone could post their answer, I would appreciate it! Thanks.

Cos^2(x) + sin^2 (x) =1 for every real value of x.(Pythagorean theorem)
What real values of x will be a solution to cos^n (x)- sin^n (x) =1, for a given positive integer n?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help!!!

For n = 2, at 0 and 180 degrees cosine squared is 1, less the zero sine at those points is 1.
For n=3, at 270 degrees, the -1 sine is cubed still negative, but the equations lesses it to positive 1, and cosine is 0 at 270.

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igloo myrtilles fourmis

Pixel

Member

Registered: 2009-11-25

Posts: 2

Re: Help!!!

Ok, so if n is even x=0 x=k*pi, and if n is odd x=0 x=3pi/2+2*k*pi???

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help!!!

Oh yes, I forgot about x = 0 if n is odd, correct.  and adding the 2pi by k is a good idea for foreverness.

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igloo myrtilles fourmis