函式關係

tanacota=1 sinacsca=1 cosaseca=1

tana=sina/cosa cota=cosa/sina

sin²a+cos²a=1 1+tan²a=sec²a 1+cot²a=csc²a

sin(a+b)=sinacosb+cosasinb

sin(a-b)=sinacosb-cosasinb

cos(a+b)=cosacosb-sinasinb

cos(a-b)=cosacosb+sinasinb

tan(a+b)=(tana+tanb)/(1-tanatanb)

tan(a-b)=(tana-tanb)/(1+tanatanb)

cot(a+b)=(cotacotb-1)/(cotb+cota)

cot(a-b)=(cotacotb+1)/(cotb-cota)

sina+sinb=2sin(a+b)/2 cos(a-b)/2

sina-sinb=2cos(a+b)/2 sin(a-b)/2

cosa+cosb=2cos(a+b)/2 cos(a-b)/2

cosa-cosb=-2sin(a+b)/2 sin(a-b)/2

tana+tanb=sin(a+b)/ cosacosb

cosasinb=1/2 [sin(a+b)-sin(a-b)]

sinacosb=1/2 [sin(a+b)+sin(a-b)]

cosacosb=1/2 [cos(a-b)+cos(a+b)]

sinasinb=1/2 [cos(a-b)-cos(a+b)]

sin2a=2sinacosa

cos2a=cos²a-sin²a=2cos²a-1=1-tan²a=2tana/(1-tan²a)

sin a/2=+/-√ (1-cosa)/2

cos a/2=+/-√ (1+cosa)/2

tan a/2=sina/(1+cosa)=(1-cosa)/sina=+/-√ (1-cosa)/(1+cosa)

cot a/2=(1+cosa)/sina=sina/(1-cosa)=+/-√ (1+cosa)/(1-cosa)

sina=2tan a/2 /(1+tan² a/2)

cosa=(1-tan² a/2) /(1+tan² a/2)

tana=2tan a/2 /(1-tan² a/2)

asinα+bcosβ=√(a²+b²)sin(α+φ),tanφ=b/a