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Ángulos Notables

Aˊngulo (∘)Aˊngulo (rad)sin⁡cos⁡tan⁡cot⁡sec⁡csc⁡0∘0010±∞1±∞15∘π126−246+242−32+36−26+230∘π61232333233245∘π42222112260∘π33212333223375∘5π126+246−242+32−36+26−290∘π210±∞0±∞1105∘7π126+24−6−24−2−3−2+3−6−26−2120∘2π332−12−3−33−2233135∘3π422−22−1−1−22150∘5π612−32−33−3−2332165∘11π126−24−6+24−2+3−2−3−6+26+2180∘π0−10±∞−1±∞195∘13π12−6−24−6+242−32+3−6+2−6−2210∘7π6−12−32333−233−2225∘5π4−22−2211−2−2240∘4π3−32−12333−2−233255∘17π12−6+24−6−242+32−3−6−2−6+2270∘3π2−10±∞0±∞−1285∘19π12−6+246−24−2−3−2+36+2−6+2300∘5π3−3212−3−332−233315∘7π4−2222−1−12−2330∘11π6−1232−33−3233−2345∘23π12−6−246+24−2+3−2−36−2−6−2360∘2π010±∞1±∞\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c:c} \text{Ángulo ($^\circ$)} & \text{Ángulo (rad)} & \sin & \cos & \tan & \cot & \sec & \csc \\ \hline 0^\circ & 0 & 0 & 1 & 0 & \pm \infty & 1 & \pm \infty \\ \hdashline 15^\circ & \frac{\pi}{12} & \frac{\sqrt{6} - \sqrt{2}}{4} & \frac{\sqrt{6} + \sqrt{2}}{4} & 2 - \sqrt{3} & 2 + \sqrt{3} & \sqrt{6} - \sqrt{2} & \sqrt{6} + \sqrt{2} \\ \hdashline 30^\circ & \frac{\pi}{6} & \frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{3} & \sqrt{3} & \frac{2\sqrt{3}}{3} & 2 \\ \hdashline 45^\circ & \frac{\pi}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 1 & 1 & \sqrt{2} & \sqrt{2} \\ \hdashline 60^\circ & \frac{\pi}{3} & \frac{\sqrt{3}}{2} & \frac{1}{2} & \sqrt{3} & \frac{\sqrt{3}}{3} & 2 & \frac{2\sqrt{3}}{3} \\ \hdashline 75^\circ & \frac{5\pi}{12} & \frac{\sqrt{6} + \sqrt{2}}{4} & \frac{\sqrt{6} - \sqrt{2}}{4} & 2 + \sqrt{3} & 2 - \sqrt{3} & \sqrt{6} + \sqrt{2} & \sqrt{6} - \sqrt{2} \\ \hdashline 90^\circ & \frac{\pi}{2} & 1 & 0 & \pm \infty & 0 & \pm \infty & 1 \\ \hdashline 105^\circ & \frac{7\pi}{12} & \frac{\sqrt{6} + \sqrt{2}}{4} & -\frac{\sqrt{6} - \sqrt{2}}{4} & -2 - \sqrt{3} & -2 + \sqrt{3} & -\sqrt{6} - \sqrt{2} & \sqrt{6} - \sqrt{2} \\ \hdashline 120^\circ & \frac{2\pi}{3} & \frac{\sqrt{3}}{2} & -\frac{1}{2} & -\sqrt{3} & -\frac{\sqrt{3}}{3} & -2 & \frac{2\sqrt{3}}{3} \\ \hdashline 135^\circ & \frac{3\pi}{4} & \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & -1 & -1 & -\sqrt{2} & \sqrt{2} \\ \hdashline 150^\circ & \frac{5\pi}{6} & \frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{3} & -\sqrt{3} & -\frac{2\sqrt{3}}{3} & 2 \\ \hdashline 165^\circ & \frac{11\pi}{12} & \frac{\sqrt{6} - \sqrt{2}}{4} & -\frac{\sqrt{6} + \sqrt{2}}{4} & -2 + \sqrt{3} & -2 - \sqrt{3} & -\sqrt{6} + \sqrt{2} & \sqrt{6} + \sqrt{2} \\ \hdashline 180^\circ & \pi & 0 & -1 & 0 & \pm \infty & -1 & \pm \infty \\ \hdashline 195^\circ & \frac{13\pi}{12} & -\frac{\sqrt{6} - \sqrt{2}}{4} & -\frac{\sqrt{6} + \sqrt{2}}{4} & 2 - \sqrt{3} & 2 + \sqrt{3} & -\sqrt{6} + \sqrt{2} & -\sqrt{6} - \sqrt{2} \\ \hdashline 210^\circ & \frac{7\pi}{6} & -\frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{3} & \sqrt{3} & -\frac{2\sqrt{3}}{3} & -2 \\ \hdashline 225^\circ & \frac{5\pi}{4} & -\frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 1 & 1 & -\sqrt{2} & -\sqrt{2} \\ \hdashline 240^\circ & \frac{4\pi}{3} & -\frac{\sqrt{3}}{2} & -\frac{1}{2} & \sqrt{3} & \frac{\sqrt{3}}{3} & -2 & -\frac{2\sqrt{3}}{3} \\ \hdashline 255^\circ & \frac{17\pi}{12} & -\frac{\sqrt{6} + \sqrt{2}}{4} & -\frac{\sqrt{6} - \sqrt{2}}{4} & 2 + \sqrt{3} & 2 - \sqrt{3} & -\sqrt{6} - \sqrt{2} & -\sqrt{6} + \sqrt{2} \\ \hdashline 270^\circ & \frac{3\pi}{2} & -1 & 0 & \pm \infty & 0 & \pm \infty & -1 \\ \hdashline 285^\circ & \frac{19\pi}{12} & -\frac{\sqrt{6} + \sqrt{2}}{4} & \frac{\sqrt{6} - \sqrt{2}}{4} & -2 - \sqrt{3} & -2 + \sqrt{3} & \sqrt{6} + \sqrt{2} & -\sqrt{6} + \sqrt{2} \\ \hdashline 300^\circ & \frac{5\pi}{3} & -\frac{\sqrt{3}}{2} & \frac{1}{2} & -\sqrt{3} & -\frac{\sqrt{3}}{3} & 2 & -\frac{2\sqrt{3}}{3} \\ \hdashline 315^\circ & \frac{7\pi}{4} & -\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & -1 & -1 & \sqrt{2} & -\sqrt{2} \\ \hdashline 330^\circ & \frac{11\pi}{6} & -\frac{1}{2} & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{3} & -\sqrt{3} & \frac{2\sqrt{3}}{3} & -2 \\ \hdashline 345^\circ & \frac{23\pi}{12} & -\frac{\sqrt{6} - \sqrt{2}}{4} & \frac{\sqrt{6} + \sqrt{2}}{4} & -2 + \sqrt{3} & -2 - \sqrt{3} & \sqrt{6} - \sqrt{2} & -\sqrt{6} - \sqrt{2} \\ \hdashline 360^\circ & 2\pi & 0 & 1 & 0 & \pm \infty & 1 & \pm \infty \\ \end{array}