Tangent of Three Right Angles
(Redirected from Tangent of 270 Degrees)
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Theorem
- $\tan 270 \degrees = \tan \dfrac {3 \pi} 2$ is undefined
where $\tan$ denotes tangent.
Proof
We have:
\(\ds \tan 270 \degrees\) | \(=\) | \(\ds \map \tan {360 \degrees - 90 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds -\tan 90 \degrees\) | Tangent of Conjugate Angle |
But from Tangent of Right Angle, $\tan 90 \degrees$ is undefined.
Hence so is $\tan 270 \degrees$.
$\blacksquare$
Also defined as
Some sources give that:
- $\tan 270 \degrees = \infty$
but this naïve approach is overly simplistic and cannot be backed up with mathematical rigour.
Also see
- Sine of Three Right Angles
- Cosine of Three Right Angles
- Cotangent of Three Right Angles
- Secant of Three Right Angles
- Cosecant of Three Right Angles
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Special angles
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles