Sinus

Sinus (lambang: sin; bahasa Inggris: sine) dalam matematika adalah perbandingan sisi segitiga yang ada di depan sudut dengan sisi miring (dengan catatan bahwa segitiga itu adalah segitiga siku-siku atau salah satu sudut segitiga itu 90^o). Perhatikan segitiga di kanan; berdasarkan definisi sinus di atas maka nilai sinus adalah

${\displaystyle \sin A={{\mbox{a}} \over {\mbox{c}}}\qquad \sin B={{\mbox{b}} \over {\mbox{c}}}}$

Nilai sinus positif di kuadran I dan II dan negatif di kuadran III dan IV.

Hubungan sinus dengan kosekan:

${\displaystyle \csc A={\frac {1}{\sin A}}\,}$

Nilai sinus sudut istimewa

	0°	15°	30°	37°	45°	53°	60°	75°	90°
Sinus	${\displaystyle 0}$	${\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}$	${\displaystyle {\frac {1}{2}}}$	${\displaystyle {\frac {3}{5}}}$	${\displaystyle {\frac {\sqrt {2}}{2}}}$	${\displaystyle {\frac {4}{5}}}$	${\displaystyle {\frac {\sqrt {3}}{2}}}$	${\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}$	${\displaystyle 1}$
Kosinus	${\displaystyle 1}$	${\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}$	${\displaystyle {\frac {\sqrt {3}}{2}}}$	${\displaystyle {\frac {4}{5}}}$	${\displaystyle {\frac {\sqrt {2}}{2}}}$	${\displaystyle {\frac {3}{5}}}$	${\displaystyle {\frac {1}{2}}}$	${\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}$	${\displaystyle 0}$
Tangen	${\displaystyle 0}$	${\displaystyle 2-{\sqrt {3}}}$	${\displaystyle {\frac {\sqrt {3}}{3}}}$	${\displaystyle {\frac {3}{4}}}$	${\displaystyle 1}$	${\displaystyle {\frac {4}{3}}}$	${\displaystyle {\sqrt {3}}}$	${\displaystyle 2+{\sqrt {3}}}$	${\displaystyle \infty }$
Kotangen	${\displaystyle \infty }$	${\displaystyle 2+{\sqrt {3}}}$	${\displaystyle {\sqrt {3}}}$	${\displaystyle {\frac {4}{3}}}$	${\displaystyle 1}$	${\displaystyle {\frac {3}{4}}}$	${\displaystyle {\frac {\sqrt {3}}{3}}}$	${\displaystyle 2-{\sqrt {3}}}$	${\displaystyle 0}$
Sekan	${\displaystyle 1}$	${\displaystyle {\sqrt {6}}-{\sqrt {2}}}$	${\displaystyle {\frac {2{\sqrt {3}}}{3}}}$	${\displaystyle {\frac {5}{4}}}$	${\displaystyle {\sqrt {2}}}$	${\displaystyle {\frac {5}{3}}}$	${\displaystyle 2}$	${\displaystyle {\sqrt {6}}+{\sqrt {2}}}$	${\displaystyle \infty }$
Kosekan	${\displaystyle \infty }$	${\displaystyle {\sqrt {6}}+{\sqrt {2}}}$	${\displaystyle 2}$	${\displaystyle {\frac {5}{3}}}$	${\displaystyle {\sqrt {2}}}$	${\displaystyle {\frac {5}{4}}}$	${\displaystyle {\frac {2{\sqrt {3}}}{3}}}$	${\displaystyle {\sqrt {6}}-{\sqrt {2}}}$	${\displaystyle 1}$