Tangent of Angle plus Straight Angle
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Theorem
- $\tan \left({x + \pi}\right) = \tan x$
Proof
\(\ds \tan \left({x + \pi}\right)\) | \(=\) | \(\ds \frac {\sin \left({x + \pi}\right)} {\cos \left({x + \pi}\right)}\) | Tangent is Sine divided by Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {-\sin x} {-\cos x}\) | Sine of Angle plus Straight Angle and Cosine of Angle plus Straight Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds \tan x\) | Tangent is Sine divided by Cosine |
$\blacksquare$
Also see
- Sine of Angle plus Straight Angle
- Cosine of Angle plus Straight Angle
- Cotangent of Angle plus Straight Angle
- Secant of Angle plus Straight Angle
- Cosecant of Angle plus Straight Angle
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I