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Geometry/Fourier Transform

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Question
Dear Prof Azeem

en.wikipedia.org/wiki/Fourier_transform
www.thefouriertransform.com
www.youtube.com/watch?v=vQLH7qTeJRM
en.wikipedia.org/wiki/Fourier_series

Can we extend Fourier transform equations to all trigonometric functions ?.

viz Tan, Cot, Sec, Cosec other than Sin, Cosine

Can the Fourier series be applied to other trigonometric  functions ?.

viz Tan, Cot, Sec, Cosec other than Sin, Cosine

Thanks & Regards,
Prashant S Akerkar

Answer
Hi Prashant,

A Fourier series is a representation of a function as a sum of sines and cosines.  This is a representation over an interval, and the function must be integrable over that interval.

The sines and cosines come from the complex exponential function.  How do you envision extending this to the other trigonometric functions?  Though the others you mentioned are quotients of sines and cosines, I do not how you expect them to be involved here.

Can you perhaps provide an example of what you mean?

Thanks for asking,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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