When is sinx+cosx+tanx+cotx+secx+cscx an integer ?
Konstantine Zelator
TL;DR
This paper analyzes the conditions under which the sum of sine, cosine, tangent, cotangent, secant, and cosecant functions equals an integer, establishing ranges where solutions exist or do not.
Contribution
It provides a complete characterization of the integer values for which the equation has solutions, including proofs of solution existence or absence.
Findings
No solutions for n between -1 and 6 inclusive.
Solutions exist for n ≥ 7 or n ≤ -2.
The solution set is explicitly described for these ranges.
Abstract
In this paper, we investigate the one-variable equation, sinx+cosx+tanx+cotx+secx+cscx=n, where n is an integer. We prove that if n lies between(inclusively) -1 and 6; then the above equation has no real number solutions. While if n is greater than or equal to 7; or less than or equal to -2, then the said equation has a nonempty solution set which we describe.
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Taxonomy
TopicsFunctional Equations Stability Results · Limits and Structures in Graph Theory · Mathematical and Theoretical Analysis