পিথাগোরাসের ত্রিকোণমিতিক উপপাদ্য

${\displaystyle \sin \theta ={\frac {\mathrm {opposite} }{\mathrm {hypotenuse} }}={\frac {b}{c}}}$

${\displaystyle \cos \theta ={\frac {\mathrm {adjacent} }{\mathrm {hypotenuse} }}={\frac {a}{c}}}$

পিথাগোরাসের উপপাদ্য থেকে,

${\displaystyle \sin ^{2}\theta +\cos ^{2}\theta ={\frac {b^{2}}{c^{2}}}+{\frac {a^{2}}{c^{2}}}={\frac {b^{2}+a^{2}}{c^{2}}}={\frac {c^{2}}{c^{2}}}=1}$

অন্যান্য সম্পর্ক

এগুলিও পিথাগোরাসের ত্রিকোণমিতিক উপপাদ্য নামে পরিচিত।^[১]

১)

${\displaystyle \tan \theta ={\frac {\mathrm {opposite} }{\mathrm {adjacent} }}={\frac {b}{a}}}$

${\displaystyle \sec \theta ={\frac {\mathrm {hypotenuse} }{\mathrm {adjacent} }}={\frac {c}{a}}}$

${\displaystyle \tan ^{2}\theta +1={\frac {b^{2}}{a^{2}}}+1={\frac {b^{2}+a^{2}}{a^{2}}}={\frac {c^{2}}{a^{2}}}=\sec ^{2}\theta }$

২)

${\displaystyle \cot \theta ={\frac {\mathrm {adjacent} }{\mathrm {opposite} }}={\frac {a}{b}}}$

${\displaystyle \csc \theta ={\frac {\mathrm {hypotenuse} }{\mathrm {opposite} }}={\frac {c}{b}}}$

${\displaystyle \cot ^{2}\theta +1={\frac {a^{2}}{b^{2}}}+1={\frac {b^{2}+a^{2}}{b^{2}}}={\frac {c^{2}}{b^{2}}}=\csc ^{2}\theta }$