On certain old and new trigonometric and hyperbolic inequalities (Q519985)
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scientific article; zbMATH DE number 6699217
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On certain old and new trigonometric and hyperbolic inequalities |
scientific article; zbMATH DE number 6699217 |
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On certain old and new trigonometric and hyperbolic inequalities (English)
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31 March 2017
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The authors obtain two-sided inequalities for trigonometric functions and hyperbolic functions. More precisely, they derive new lower and upper bounds for \(\tan\frac{x}{2}\) and \(\frac{\sin x}{x}\), as well as the hyperbolic counterpart of the latter. Some monotonicity relations between power series and between functions are used in the proofs.
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trigonometric functions
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hyperbolic functions
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