high School⏱ 3 min

Tangent Function

Tangent function visualization

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-1.5π-1π-0.5π00.5π1π1.5π
θ = 45°
 an heta=\ rac extopposite extadjacent\ an\ heta = \ rac{\ ext{opposite}}{\ ext{adjacent}}
tan⁡(45°)=sin⁡45°cos⁡45°=1.0000\tan(45°) = \frac{\sin 45°}{\cos 45°} = 1.0000

tan(θ) = sin/cos. As θ→90°, cosine→0, so tangent→∞. Yellow dashed lines are asymptotes at ±90°, ±270°...