More On Mixing Trig Functions

I’ve had several occasions in face-to-face tutoring lately to refer to a past post on mixing (that is, composition) of trig and inverse trig functions. Several recent questions have touched directly or indirectly on this same general idea and extended it, so I thought I’d post them.

Three Trigonometric Inequalities

(A new question of the week) We often solve basic trigonometric equations; but a recent set of questions dealt with challenging trigonometric inequalities, which bring with them a new set of issues. We’ll look at several of those here, which combine trig with polynomials, rational functions, and more. Each will illustrate something new to watch …

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Euler’s Formula: Complex Numbers as Exponents

Last week we explored how the polar form of complex numbers gives multiplication a simple geometric meaning. Here we’ll go one more step, and express polar form exponentially, which makes DeMoivre’s theorem trivial, and gives us a simple notation to replace “cis”.