leehuan Well-Known Member Joined May 31, 2014 Messages 5,805 Gender Male HSC 2015 May 24, 2016 #41 Yeah if the constant marks the greatest number of a Pythagorean triple it may be faster to use the auxiliary angle method.
Yeah if the constant marks the greatest number of a Pythagorean triple it may be faster to use the auxiliary angle method.
Paradoxica -insert title here- Joined Jun 19, 2014 Messages 2,556 Location Outside reality Gender Male HSC 2016 May 24, 2016 #42 Drongoski said: That's interesting. I have not investigated, but I noticed that in both integrals, {3,4,5} and {5,12,13} are Pythagorean Triples. Click to expand... It's because of the Auxiliary Transformation takes √a2+b2 for the harmonic coefficient, but since it is a Pythagorean Triple, that coefficient is, by definition, c.
Drongoski said: That's interesting. I have not investigated, but I noticed that in both integrals, {3,4,5} and {5,12,13} are Pythagorean Triples. Click to expand... It's because of the Auxiliary Transformation takes √a2+b2 for the harmonic coefficient, but since it is a Pythagorean Triple, that coefficient is, by definition, c.
Paradoxica -insert title here- Joined Jun 19, 2014 Messages 2,556 Location Outside reality Gender Male HSC 2016 May 24, 2016 #43 leehuan said: Yeah if the constant marks the greatest number of a Pythagorean triple it may be faster to use the auxiliary angle method. Click to expand... But in any case, it doesn't need to be a Pythagorean Triple. As long as asinx + bcosx + c satisfies a2+b2=c2, the Auxiliary Transformation and Tangent Half Angle Substitution are guaranteed to be nice.
leehuan said: Yeah if the constant marks the greatest number of a Pythagorean triple it may be faster to use the auxiliary angle method. Click to expand... But in any case, it doesn't need to be a Pythagorean Triple. As long as asinx + bcosx + c satisfies a2+b2=c2, the Auxiliary Transformation and Tangent Half Angle Substitution are guaranteed to be nice.
leehuan Well-Known Member Joined May 31, 2014 Messages 5,805 Gender Male HSC 2015 May 24, 2016 #44 Paradoxica said: But in any case, it doesn't need to be a Pythagorean Triple. As long as asinx + bcosx + c satisfies a2+b2=c2, the Auxiliary Transformation and Tangent Half Angle Substitution are guaranteed to be nice. Click to expand... Yeah basically point is to use one or the other
Paradoxica said: But in any case, it doesn't need to be a Pythagorean Triple. As long as asinx + bcosx + c satisfies a2+b2=c2, the Auxiliary Transformation and Tangent Half Angle Substitution are guaranteed to be nice. Click to expand... Yeah basically point is to use one or the other