Tingkat trigonometri

Fungsi dasar:

{\displaystyle sinA={\frac {a}{c}}}{\displaystyle cosA={\frac {b}{c}}}{\displaystyle tanA={\frac {sinA}{cosA}}={\frac {a}{b}}}{\displaystyle cotA={\frac {1}{tanA}}={\frac {cosA}{sinA}}={\frac {b}{a}}}{\displaystyle secA={\frac {1}{cosA}}={\frac {c}{b}}}{\displaystyle cscA={\frac {1}{sinA}}={\frac {c}{a}}}

Identitas trigonometri

{\displaystyle sin^{2}A+cos^{2}A=1}{\displaystyle 1+tan^{2}A={\frac {1}{cos^{2}A}}=sec^{2}A}{\displaystyle 1+cot^{2}A={\frac {1}{sin^{2}A}}=csc^{2}A}

Rumus jumlah dan selisih sudut

{\displaystyle sin(A+B)=sinAcosB+cosAsinB}{\displaystyle sin(A-B)=sinAcosB-cosAsinB}{\displaystyle cos(A+B)=cosAcosB-sinAsinB}{\displaystyle cos(A-B)=cosAcosB+sinAsinB}{\displaystyle tan(A+B)={\frac {tanA+tanB}{1-tanAtanB}}}{\displaystyle tan(A-B)={\frac {tanA-tanB}{1+tanAtanB}}}

Rumus perkalian trigonometri

{\displaystyle 2sinAcosB=sin(A+B)+sin(A-B)}{\displaystyle 2cosAsinB=sin(A+B)-sin(A-B)}{\displaystyle 2cosAcosB=cos(A+B)+cos(A-B)}{\displaystyle 2sinAsinB=-cos(A+B)+cos(A-B)}

Rumus jumlah dan selisih trigonometri

{\displaystyle sinA+sinB=2sin{\frac {1}{2}}(A+B)cos{\frac {1}{2}}(A-B)}{\displaystyle sinA-sinB=2cos{\frac {1}{2}}(A+B)sin{\frac {1}{2}}(A-B)}{\displaystyle cosA+cosB=2cos{\frac {1}{2}}(A+B)cos{\frac {1}{2}}(A-B)}{\displaystyle cosA-cosB=-2sin{\frac {1}{2}}(A+B)sin{\frac {1}{2}}(A-B)}

Rumus sudut rangkap dua

{\displaystyle sin2A=2sinAcosA}{\displaystyle cos2A=cos^{2}A-sin^{2}A=1-2sin^{2}A=2cos^{2}A-1}{\displaystyle tan2A={\frac {2tanA}{1-tan^{2}A}}={\frac {2cotA}{cot^{2}A-1}}={\frac {2}{cotA-tanA}}}

Rumus sudut rangkap tiga

{\displaystyle sin3A=3sinA-4sin^{3}A}{\displaystyle cos3A=4cos^{3}A-3cosA}

Rumus setengah sudut

{\displaystyle sin{\frac {A}{2}}=\pm {\sqrt {\frac {1-cosA}{2}}}}{\displaystyle cos{\frac {A}{2}}=\pm {\sqrt {\frac {1+cosA}{2}}}}{\displaystyle tan{\frac {A}{2}}=\pm {\sqrt {\frac {1-cosA}{1+cosA}}}={\frac {sinA}{1+cosA}}={\frac {1-cosA}{sinA}}}