Tangen

Tangen (lambang tg, tan; bahasa Belanda: tangens; bahasa Inggris: tangent) dalam matematika adalah perbandingan sisi segitiga yang ada di depan sudut dengan sisi segitiga yang terletak di sudut (dengan catatan bahwa segitiga itu adalah segitiga siku-siku atau salah satu sudut segitiga itu 90^o).

Berdasarkan segitiga pada ilustrator (di kanan), berdasarkan definisi tangen, di atas maka nilai tangen adalah

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

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

Hubungan tangen dengan kotangen:

${\displaystyle \cot A={\frac {1}{\tan A}}\,}$

Hubungan nilai tangen dengan nilai sinus dan kosinus

${\displaystyle \tan A={\frac {sinA}{cosA}}\,}$

Nilai tangen sudut istimewa

	0°	8°	15°	16°	18°	30°	37°	45°	53°	60°	72°	74°	75°	82°	90°
Sinus	${\displaystyle 0}$	${\displaystyle {\frac {\sqrt {2}}{10}}}$	${\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}$	${\displaystyle {\frac {7}{25}}}$	${\displaystyle {\frac {-1+{\sqrt {5}}}{4}}}$	${\displaystyle {\frac {1}{2}}}$	${\displaystyle {\frac {3}{5}}}$	${\displaystyle {\frac {\sqrt {2}}{2}}}$	${\displaystyle {\frac {4}{5}}}$	${\displaystyle {\frac {\sqrt {3}}{2}}}$	${\displaystyle {\frac {\sqrt {10+2{\sqrt {5}}}}{4}}}$	${\displaystyle {\frac {24}{25}}}$	${\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}$	${\displaystyle {\frac {7{\sqrt {2}}}{10}}}$	${\displaystyle 1}$
Kosinus	${\displaystyle 1}$	${\displaystyle {\frac {7{\sqrt {2}}}{10}}}$	${\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}$	${\displaystyle {\frac {24}{25}}}$	${\displaystyle {\frac {\sqrt {10+2{\sqrt {5}}}}{4}}}$	${\displaystyle {\frac {\sqrt {3}}{2}}}$	${\displaystyle {\frac {4}{5}}}$	${\displaystyle {\frac {\sqrt {2}}{2}}}$	${\displaystyle {\frac {3}{5}}}$	${\displaystyle {\frac {1}{2}}}$	${\displaystyle {\frac {-1+{\sqrt {5}}}{4}}}$	${\displaystyle {\frac {7}{25}}}$	${\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}$	${\displaystyle {\frac {\sqrt {2}}{10}}}$	${\displaystyle 0}$
Tangen	${\displaystyle 0}$	${\displaystyle {\frac {1}{7}}}$	${\displaystyle 2-{\sqrt {3}}}$	${\displaystyle {\frac {7}{24}}}$	${\displaystyle {\frac {(1+{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{4}}}$	${\displaystyle {\frac {\sqrt {3}}{3}}}$	${\displaystyle {\frac {3}{4}}}$	${\displaystyle 1}$	${\displaystyle {\frac {4}{3}}}$	${\displaystyle {\sqrt {3}}}$	${\displaystyle {\frac {(-1+{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{10+2{\sqrt {5}}}}}$	${\displaystyle {\frac {24}{7}}}$	${\displaystyle 2+{\sqrt {3}}}$	${\displaystyle 7}$	${\displaystyle \infty }$
Kotangen	${\displaystyle \infty }$	${\displaystyle 7}$	${\displaystyle 2+{\sqrt {3}}}$	${\displaystyle {\frac {24}{7}}}$	${\displaystyle {\frac {(-1+{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{10+2{\sqrt {5}}}}}$	${\displaystyle {\sqrt {3}}}$	${\displaystyle {\frac {4}{3}}}$	${\displaystyle 1}$	${\displaystyle {\frac {3}{4}}}$	${\displaystyle {\frac {\sqrt {3}}{3}}}$	${\displaystyle {\frac {(1+{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{4}}}$	${\displaystyle {\frac {7}{24}}}$	${\displaystyle 2-{\sqrt {3}}}$	${\displaystyle {\frac {1}{7}}}$	${\displaystyle 0}$
Sekan	${\displaystyle 1}$	${\displaystyle {\frac {5{\sqrt {2}}}{7}}}$	${\displaystyle {\sqrt {6}}-{\sqrt {2}}}$	${\displaystyle {\frac {25}{24}}}$	${\displaystyle {\frac {4{\sqrt {10+2{\sqrt {5}}}}}{10+2{\sqrt {5}}}}}$	${\displaystyle {\frac {2{\sqrt {3}}}{3}}}$	${\displaystyle {\frac {5}{4}}}$	${\displaystyle {\sqrt {2}}}$	${\displaystyle {\frac {5}{3}}}$	${\displaystyle 2}$	${\displaystyle 1+{\sqrt {5}}}$	${\displaystyle {\frac {25}{7}}}$	${\displaystyle {\sqrt {6}}+{\sqrt {2}}}$	${\displaystyle 5{\sqrt {2}}}$	${\displaystyle \infty }$
Kosekan	${\displaystyle \infty }$	${\displaystyle 5{\sqrt {2}}}$	${\displaystyle {\sqrt {6}}+{\sqrt {2}}}$	${\displaystyle {\frac {25}{7}}}$	${\displaystyle 1+{\sqrt {5}}}$	${\displaystyle 2}$	${\displaystyle {\frac {5}{3}}}$	${\displaystyle {\sqrt {2}}}$	${\displaystyle {\frac {5}{4}}}$	${\displaystyle {\frac {2{\sqrt {3}}}{3}}}$	${\displaystyle {\frac {4{\sqrt {10+2{\sqrt {5}}}}}{10+2{\sqrt {5}}}}}$	${\displaystyle {\frac {25}{24}}}$	${\displaystyle {\sqrt {6}}-{\sqrt {2}}}$	${\displaystyle {\frac {5{\sqrt {2}}}{7}}}$	${\displaystyle 1}$