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2003•Victoria University Research Repository (Victoria University)Open access

Three Inequalities Involving Hyperbolically Trigonometric Functions

Chao-Ping Chen, Jian-Wei Zhao, Feng Qi

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Abstract

In the short note, by using mathematical induction and infinite product representations of the cosine function, hyperbolic sine function and hyperbolic cosine function, three inequalities for the cosine function, hyperbolic sine function and hyperbolic cosine function are established.

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What this paper is about

In the short note, by using mathematical induction and infinite product representations of the cosine function, hyperbolic sine function and hyperbolic cosine function, three inequalities for the cosine function, hyperbolic sine function and hyperbolic cosine function are established.

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OpenAlex reports 23 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In the short note, by using mathematical induction and infinite product representations of the cosine function, hyperbolic sine function and hyperbolic cosine function, three inequalities for the cosine function, hyperbolic sine function and hyperbolic cosine function are established.

Key concepts: Trigonometric functions, Sine, Hyperbolic function, Differentiation of trigonometric functions, Mathematics, Pythagorean trigonometric identity, Function (biology), Mathematical analysis

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