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Modular
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Baze

Modular Exponent

Calculează puteri mari sau inversul modular.

Calculator Fracții

Adună, scade, înmulțește sau împarte fracții.
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Combinări & Aranjamente

\(C(n,k)=\frac{n!}{k!(n-k)!}\) · \(A(n,k)=\frac{n!}{(n-k)!}\)

Numere Prime

Generează toate numerele prime ≤ limită.

Triplete Pitagorice

Primitive \((a,b,c)\) cu \(a^2+b^2=c^2\), ordonate după \(c\).

Divizori & Indicatorul lui Euler

Descompunere în factori primi, numărul și suma divizorilor, φ(n).

Valori Trigonometrice Exacte

Exacte din 15° în 15°, pe cadrane.
Cadranul I · 0° → 90°
°0153045607590
\(\pi\)0\(\frac{\pi}{12}\)\(\frac{\pi}{6}\)\(\frac{\pi}{4}\)\(\frac{\pi}{3}\)\(\frac{5\pi}{12}\)\(\frac{\pi}{2}\)
\(\approx\)0.0000.2620.5240.7851.0471.3091.571
\(\sin\)0\(\frac{\sqrt{6}-\sqrt{2}}{4}\)\(\frac12\)\(\frac{\sqrt2}{2}\)\(\frac{\sqrt3}{2}\)\(\frac{\sqrt{6}+\sqrt{2}}{4}\)1
\(\cos\)1\(\frac{\sqrt{6}+\sqrt{2}}{4}\)\(\frac{\sqrt3}{2}\)\(\frac{\sqrt2}{2}\)\(\frac12\)\(\frac{\sqrt{6}-\sqrt{2}}{4}\)0
\(\tan\)0\(2-\sqrt3\)\(\frac{\sqrt3}{3}\)1\(\sqrt3\)\(2+\sqrt3\)∞
Cadranul II · 90° → 180°
°90105120135150165180
\(\pi\)\(\frac{\pi}{2}\)\(\frac{7\pi}{12}\)\(\frac{2\pi}{3}\)\(\frac{3\pi}{4}\)\(\frac{5\pi}{6}\)\(\frac{11\pi}{12}\)\(\pi\)
\(\approx\)1.5711.8332.0942.3562.6182.8803.142
\(\sin\)1\(\frac{\sqrt{6}+\sqrt{2}}{4}\)\(\frac{\sqrt3}{2}\)\(\frac{\sqrt2}{2}\)\(\frac12\)\(\frac{\sqrt{6}-\sqrt{2}}{4}\)0
\(\cos\)0\(-\frac{\sqrt{6}-\sqrt{2}}{4}\)\(-\frac12\)\(-\frac{\sqrt2}{2}\)\(-\frac{\sqrt3}{2}\)\(-\frac{\sqrt{6}+\sqrt{2}}{4}\)\(-1\)
\(\tan\)∞\(-(2+\sqrt3)\)\(-\sqrt3\)\(-1\)\(-\frac{\sqrt3}{3}\)\(-(2-\sqrt3)\)0
Cadranul III · 180° → 270°
°180195210225240255270
\(\pi\)\(\pi\)\(\frac{13\pi}{12}\)\(\frac{7\pi}{6}\)\(\frac{5\pi}{4}\)\(\frac{4\pi}{3}\)\(\frac{17\pi}{12}\)\(\frac{3\pi}{2}\)
\(\approx\)3.1423.4033.6653.9274.1894.4514.712
\(\sin\)0\(-\frac{\sqrt{6}-\sqrt{2}}{4}\)\(-\frac12\)\(-\frac{\sqrt2}{2}\)\(-\frac{\sqrt3}{2}\)\(-\frac{\sqrt{6}+\sqrt{2}}{4}\)\(-1\)
\(\cos\)\(-1\)\(-\frac{\sqrt{6}+\sqrt{2}}{4}\)\(-\frac{\sqrt3}{2}\)\(-\frac{\sqrt2}{2}\)\(-\frac12\)\(-\frac{\sqrt{6}-\sqrt{2}}{4}\)0
\(\tan\)0\(2-\sqrt3\)\(\frac{\sqrt3}{3}\)1\(\sqrt3\)\(2+\sqrt3\)∞
Cadranul IV · 270° → 360°
°270285300315330345360
\(\pi\)\(\frac{3\pi}{2}\)\(\frac{19\pi}{12}\)\(\frac{5\pi}{3}\)\(\frac{7\pi}{4}\)\(\frac{11\pi}{6}\)\(\frac{23\pi}{12}\)\(2\pi\)
\(\approx\)4.7124.9745.2365.4985.7606.0216.283
\(\sin\)\(-1\)\(-\frac{\sqrt{6}+\sqrt{2}}{4}\)\(-\frac{\sqrt3}{2}\)\(-\frac{\sqrt2}{2}\)\(-\frac12\)\(-\frac{\sqrt{6}-\sqrt{2}}{4}\)0
\(\cos\)0\(\frac{\sqrt{6}-\sqrt{2}}{4}\)\(\frac12\)\(\frac{\sqrt2}{2}\)\(\frac{\sqrt3}{2}\)\(\frac{\sqrt{6}+\sqrt{2}}{4}\)1
\(\tan\)∞\(-(2+\sqrt3)\)\(-\sqrt3\)\(-1\)\(-\frac{\sqrt3}{3}\)\(-(2-\sqrt3)\)0

Formule Trigonometrice

⚛ Formula Fundamentală
① \(\sin^2\alpha + \cos^2\alpha = 1\)
② \(1 + \mathrm{tg}^2\alpha = \frac{1}{\cos^2\alpha}\)
③ \(1 + \mathrm{ctg}^2\alpha = \frac{1}{\sin^2\alpha}\)
④ \(\mathrm{tg}\alpha \cdot \mathrm{ctg}\alpha = 1\)
⑤ \(\mathrm{tg}\alpha = \frac{\sin\alpha}{\cos\alpha} \quad,\quad \mathrm{ctg}\alpha = \frac{\cos\alpha}{\sin\alpha}\)
📊 Semnele Funcțiilor pe Cadrane
CadranUnghisincostgctg
I0° – 90°++++
II90° – 180°+−−−
III180° – 270°−−++
IV270° – 360°−+−−
🔄 Reducere la Cadranul I

Regula cheie: dacă argumentul e \(\frac{\pi}{2} \pm \alpha\) sau \(\frac{3\pi}{2} \pm \alpha\) → funcția se schimbă (\(\sin \leftrightarrow \cos\), \(\mathrm{tg} \leftrightarrow \mathrm{ctg}\))
dacă argumentul e \(\pi \pm \alpha\) sau \(2\pi \pm \alpha\) → funcția rămâne aceeași; semnul depinde de cadranul expresiei.

Expresiesincostgctg
\(\frac{\pi}{2} - \alpha\)\(\cos \alpha\)\(\sin \alpha\)\(\mathrm{ctg} \alpha\)\(\mathrm{tg} \alpha\)
\(\frac{\pi}{2} + \alpha\)\(\cos \alpha\)\(-\sin \alpha\)\(-\mathrm{ctg} \alpha\)\(-\mathrm{tg} \alpha\)
\(\pi - \alpha\)\(\sin \alpha\)\(-\cos \alpha\)\(-\mathrm{tg} \alpha\)\(-\mathrm{ctg} \alpha\)
\(\pi + \alpha\)\(-\sin \alpha\)\(-\cos \alpha\)\(\mathrm{tg} \alpha\)\(\mathrm{ctg} \alpha\)
\(\frac{3\pi}{2} - \alpha\)\(-\cos \alpha\)\(-\sin \alpha\)\(\mathrm{ctg} \alpha\)\(\mathrm{tg} \alpha\)
\(\frac{3\pi}{2} + \alpha\)\(-\cos \alpha\)\(\sin \alpha\)\(-\mathrm{ctg} \alpha\)\(-\mathrm{tg} \alpha\)
\(2\pi - \alpha\)\(-\sin \alpha\)\(\cos \alpha\)\(-\mathrm{tg} \alpha\)\(-\mathrm{ctg} \alpha\)
\(2\pi + \alpha\)\(\sin \alpha\)\(\cos \alpha\)\(\mathrm{tg} \alpha\)\(\mathrm{ctg} \alpha\)
📐 Formule de Bază
➕  Suma  (\(\alpha + \beta\))
\(\sin(\alpha+\beta) =\) \(\sin\alpha\cos\beta + \cos\alpha\sin\beta\)
\(\cos(\alpha+\beta) =\) \(\cos\alpha\cos\beta - \sin\alpha\sin\beta\)
\(\mathrm{tg}(\alpha+\beta) =\) \(\frac{\mathrm{tg}\alpha + \mathrm{tg}\beta}{1 - \mathrm{tg}\alpha\mathrm{tg}\beta}\)
\(\mathrm{ctg}(\alpha+\beta) =\) \(\frac{\mathrm{ctg}\alpha\mathrm{ctg}\beta - 1}{\mathrm{ctg}\beta + \mathrm{ctg}\alpha}\)
➖  Diferența  (\(\alpha - \beta\))
\(\sin(\alpha-\beta) =\) \(\sin\alpha\cos\beta - \cos\alpha\sin\beta\)
\(\cos(\alpha-\beta) =\) \(\cos\alpha\cos\beta + \sin\alpha\sin\beta\)
\(\mathrm{tg}(\alpha-\beta) =\) \(\frac{\mathrm{tg}\alpha - \mathrm{tg}\beta}{1 + \mathrm{tg}\alpha\mathrm{tg}\beta}\)
\(\mathrm{ctg}(\alpha-\beta) =\) \(\frac{\mathrm{ctg}\alpha\mathrm{ctg}\beta + 1}{\mathrm{ctg}\beta - \mathrm{ctg}\alpha}\)
×2  Unghi Dublu  (\(2\alpha\))
\(\sin 2\alpha =\) \(2\sin\alpha\cos\alpha\)
\(\cos 2\alpha =\) \(\cos^2\alpha - \sin^2\alpha = 2\cos^2\alpha - 1 = 1 - 2\sin^2\alpha\)
\(\mathrm{tg} 2\alpha =\) \(\frac{2\mathrm{tg}\alpha}{1 - \mathrm{tg}^2\alpha}\)
\(\mathrm{ctg} 2\alpha =\) \(\frac{\mathrm{ctg}^2\alpha - 1}{2\mathrm{ctg}\alpha}\)
×3  Unghi Triplu  (\(3\alpha\))
\(\sin 3\alpha =\) \(3\sin\alpha - 4\sin^3\alpha\)
\(\cos 3\alpha =\) \(4\cos^3\alpha - 3\cos\alpha\)
\(\mathrm{tg} 3\alpha =\) \(\frac{3\mathrm{tg}\alpha - \mathrm{tg}^3\alpha}{1 - 3\mathrm{tg}^2\alpha}\)
\(\mathrm{ctg} 3\alpha =\) \(\frac{\mathrm{ctg}^3\alpha - 3\mathrm{ctg}\alpha}{3\mathrm{ctg}^2\alpha - 1}\)
÷2  Unghi pe Jumătate  (\(\alpha/2\))
\(\sin(\alpha/2) =\) \(\pm\sqrt{\frac{1 - \cos\alpha}{2}}\)
\(\cos(\alpha/2) =\) \(\pm\sqrt{\frac{1 + \cos\alpha}{2}}\)
\(\mathrm{tg}(\alpha/2) =\) \(\pm\sqrt{\frac{1-\cos\alpha}{1+\cos\alpha}} = \frac{\sin\alpha}{1+\cos\alpha} = \frac{1-\cos\alpha}{\sin\alpha}\)
\(\mathrm{ctg}(\alpha/2) =\) \(\pm\sqrt{\frac{1+\cos\alpha}{1-\cos\alpha}} = \frac{\sin\alpha}{1-\cos\alpha} = \frac{1+\cos\alpha}{\sin\alpha}\)

Conversie Baze de Numerație

Transformă numere între bazele 2–16. Suportă 0-9 și A-F.