- #1
Astro
- 48
- 1
When using trigonometric substitution in calculus you're supposed to always keep in mind the domain of the angle. In the case of √(x2-a2) (where "a" is a number >0) you use x=a⋅arcsec Θ for the substitution.
For trigonometric substitution, textbooks state that the domain of Θ must be {0≤Θ<π/2} ∪ {π/2<Θ≤π} when using the x=a⋅arcsec Θ substitution. Some textbooks alternatively give the allowable domain as {0≤Θ<π/2} ∪ {π≤Θ<3π/2} instead. In either case, there are issues which don't seem to make sense to me.
Please see the attached PDF file for my questions.
Thank you.
For trigonometric substitution, textbooks state that the domain of Θ must be {0≤Θ<π/2} ∪ {π/2<Θ≤π} when using the x=a⋅arcsec Θ substitution. Some textbooks alternatively give the allowable domain as {0≤Θ<π/2} ∪ {π≤Θ<3π/2} instead. In either case, there are issues which don't seem to make sense to me.
Please see the attached PDF file for my questions.
Thank you.