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(1)一般形： y = a x 2 + b x + c {\displaystyle y=ax^{2}+bx+c} (2)標準形： y = a ( x − p ) 2 + q {\displaystyle y=a(x-p)^{2}+q}
(5) tan θ = a b {\displaystyle \tan \theta ={\frac {a}{b}}} sin θ = a c {\displaystyle \sin \theta ={\frac {a}{c}}} cos θ = b c {\displaystyle \cos \theta ={\frac {b}{c}}} (6) cot θ = b a {\displaystyle \cot \theta ={\frac {b}{a}}} c o s e c θ = c a {\displaystyle cosec\theta ={\frac {c}{a}}} sec θ = c b {\displaystyle \sec \theta ={\frac {c}{b}}} (7) sin 2 θ + cos 2 θ = 1 {\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1} tan θ = s i n θ c o s θ {\displaystyle \tan \theta ={\frac {sin\theta }{cos\theta }}} t a n 2 θ + 1 = 1 c o s 2 θ {\displaystyle tan^{2}\theta +1={\frac {1}{cos^{2}\theta }}} (8) s i n ( 90 − θ ) = c o s θ {\displaystyle sin(90-\theta )=cos\theta } c o s ( 90 − θ ) = s i n θ {\displaystyle cos(90-\theta )=sin\theta } t a n ( 90 − θ ) = c o t θ = 1 t a n θ {\displaystyle tan(90-\theta )=cot\theta ={\frac {1}{tan\theta }}} (9) s i n ( 90 + θ ) = c o s θ {\displaystyle sin(90+\theta )=cos\theta } c o s ( 90 + θ ) = − s i n θ {\displaystyle cos(90+\theta )=-sin\theta } t a n ( 90 − θ ) = − c o s θ s i n θ = − 1 t a n θ {\displaystyle tan(90-\theta )=-{\frac {cos\theta }{sin\theta }}=-{\frac {1}{tan\theta }}} (10) s i n ( 180 + θ ) = s i n θ {\displaystyle sin(180+\theta )=sin\theta } c o s ( 180 + θ ) = − c o s θ {\displaystyle cos(180+\theta )=-cos\theta } t a n ( 180 − θ ) = − s i n θ c o s θ = − tan θ {\displaystyle tan(180-\theta )=-{\frac {sin\theta }{cos\theta }}=-\tan \theta } (11) s i n ( 180 + θ ) = − s i n θ {\displaystyle sin(180+\theta )=-sin\theta } c o s ( 180 + θ ) = − c o s θ {\displaystyle cos(180+\theta )=-cos\theta } t a n ( 180 − θ ) = − s i n θ − c o s θ = tan θ {\displaystyle tan(180-\theta )={\frac {-sin\theta }{-cos\theta }}=\tan \theta } (12) s i n ( − θ ) = − s i n θ {\displaystyle sin(-\theta )=-sin\theta } c o s ( − θ ) = c o s θ {\displaystyle cos(-\theta )=cos\theta } t a n ( − θ ) = − tan θ {\displaystyle tan(-\theta )=-\tan \theta }
(13) a s i n A = b s i n B = c s i n C = 2 R {\displaystyle {\frac {a}{sinA}}={\frac {b}{sinB}}={\frac {c}{sinC}}=2R}
(14) a 2 = b 2 + c 2 − 2 b c cos A {\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos A} (15) b 2 = c 2 + a 2 − 2 c a cos B {\displaystyle b^{2}=c^{2}+a^{2}-2ca\cos B} (16) c 2 = a 2 + b 2 − 2 a b cos C {\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos C} (17)14の変形： cos A = b 2 + c 2 − a 2 2 b c {\displaystyle \cos A={b^{2}+c^{2}-a^{2} \over 2bc}} (18)14の変形： cos B = c 2 + a 2 − b 2 2 c a {\displaystyle \cos B={c^{2}+a^{2}-b^{2} \over 2ca}} (19)14の変形： cos C = a 2 + b 2 − c 2 2 a b {\displaystyle \cos C={a^{2}+b^{2}-c^{2} \over 2ab}}
(20) S = 1 2 b c sin A = 1 2 c a sin B = 1 2 a b sin C {\displaystyle S={1 \over 2}bc\sin A={1 \over 2}ca\sin B={1 \over 2}ab\sin C}
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