Tangent of 45 Degrees
Theorem
- $\tan 45 \degrees = \tan \dfrac \pi 4 = 1$
where $\tan$ denotes tangent.
Proof
| \(\ds \tan 45 \degrees\) | \(=\) | \(\ds \frac {\sin 45 \degrees} {\cos 45 \degrees}\) | Tangent is Sine divided by Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\frac {\sqrt 2} 2} {\frac {\sqrt 2} 2}\) | Sine of $45 \degrees$ and Cosine of $45 \degrees$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1\) | dividing top and bottom by $\sqrt 2 / 2$ |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trigonometric function
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trigonometric function
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $12$: Trigonometric formulae: Trigonometric values for some special angles
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $14$: Trigonometric formulae: Trigonometric values for some special angles