A Generalization of the Angle Doubling Formulas for Trigonometric Functions
| Autor: | Gaston Brouwer |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pythagorean trigonometric identity
General Mathematics 010102 general mathematics Mathematical analysis Differentiation of trigonometric functions Trigonometric integral Trigonometric polynomial 01 natural sciences Integration using Euler's formula symbols.namesake symbols Trigonometric functions Inverse trigonometric functions Sine 0101 mathematics Mathematics |
| Zdroj: | Mathematics Magazine. 90:12-18 |
| ISSN: | 1930-0980 0025-570X |
| DOI: | 10.4169/math.mag.90.1.12 |
| Popis: | SummaryThe angle doubling formula sin 2θ = 2 sin θ cos θ for the sine function is well known. By replacing the cosine in this formula with sin (π/2 - θ), we see that sin 2θ can be written as the product of two sine functions where the second sine function is obtained from the basic sine function by only using a phase shift of the angle θ and a reflection about the horizontal axis. In this paper, we will show that, for any natural number n, sin nθ can be written as the product of n sine functions involving only phase shifts of the angle θ and a possible reflection about the horizontal axis. Similar formulas will be derived for the cosine and tangent functions. |
| Databáze: | OpenAIRE |
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