Tag: Series: Trigonometric Identities as Functional Equations

Math

Sine Angle Addition Functional Equation 2

Post author By Nihal Uppugunduri
Post date January 26, 2023
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In this post, we continue the discussion from this post, where we investigate the sine angle addition functional equation

$\displaystyle f(a + b) = f(a)f\left( \frac{\pi}{2} - b \right) + f\left( \frac{\pi}{2} - a \right)f(b).$

Tags Hidden From Main Subject Pages, Series: Trigonometric Identities as Functional Equations, Studies

Math

Sine Angle Addition Functional Equation

Post author By Nihal Uppugunduri
Post date January 11, 2023
No Comments on Sine Angle Addition Functional Equation

In this post, we investigate further the sine angle addition functional equation that I introduced in a previous post, Trigonometric Identities as Functional Equations. (See the work done there before reading this post.) Specifically, the question is to find all functions $f$ such that

$\displaystyle f(a + b) = f(a)f\left( \frac{\pi}{2} - b \right) + f\left( \frac{\pi}{2} - a \right)f(b).$

Tags Hidden From Main Subject Pages, Series: Trigonometric Identities as Functional Equations, Studies

Math

Trigonometric Identities as Functional Equations

Post author By Nihal Uppugunduri
Post date November 22, 2022
No Comments on Trigonometric Identities as Functional Equations

We take some basic trigonometric identities and essentially ask whether trigonometric functions are the only ones that satisfy these identities. In other words, what are all the functions that satisfy a given trigonometric identity? Thus, we take trigonometric identities and use them as functional equation problems.

Tags Series: Trigonometric Identities as Functional Equations, Studies