關於銳角三角函式的數學公式
兩角和與差的三角函式:
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)
三角和的三角函式:
sin(++)=sincoscos+cossincos+coscossin-sinsinsin
cos(++)=coscoscos-cossinsin-sincossin-sinsincos
tan(++)=(tan+tan+tan-tantantan)/(1-tantan-tantan-tantan)
輔助角公式:
Asin+Bcos=(A^2+B^2)^(1/2)sin(+t),其中
sint=B/(A^2+B^2)^(1/2)
cost=A/(A^2+B^2)^(1/2)
tant=B/A
Asin+Bcos=(A^2+B^2)^(1/2)cos(-t),tant=A/B
倍角公式:
sin(2)=2sincos=2/(tan+cot)
cos(2)=cos^2()-sin^2()=2cos^2()-1=1-2sin^2()
tan(2)=2tan/[1-tan^2()]
三倍角公式:
sin(3)=3sin-4sin^3()
cos(3)=4cos^3()-3cos