完整三角函数公式表
完整三角函数公式表?
完整三角函数公式表?
两角和公式
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)
倍角公式
tan2A = 2tanA/(1-tan² A)
Sin2A=2SinA•CosA
Cos2A = Cos^2 A--Sin² A
=2Cos² A—1
=1—2sin^2 A
三倍角公式
sin3A = 3sinA-4(sinA)³
cos3A = 4(cosA)³ -3cosA
tan3a = tan a • tan(π/3 a)• tan(π/3-a)
半角公式
sin(A/2) = √{(1--cosA)/2}
cos(A/2) = √{(1 cosA)/2}
tan(A/2) = √{(1--cosA)/(1 cosA)}
cot(A/2) = √{(1 cosA)/(1-cosA)} ?
tan(A/2) = (1--cosA)/sinA=sinA/(1 cosA)
和差化积
sin(a) sin(b) = 2sin[(a b)/2]cos[(a-b)/2]
sin(a)-sin(b) = 2cos[(a b)/2]sin[(a-b)/2]
cos(a) cos(b) = 2cos[(a b)/2]cos[(a-b)/2]
cos(a)-cos(b) = -2sin[(a b)/2]sin[(a-b)/2]
tanA tanB=sin(A B)/cosAcosB
积化和差
sin(a)sin(b) = -1/2*[cos(a b)-cos(a-b)]
cos(a)cos(b) = 1/2*[cos(a b) cos(a-b)]
sin(a)cos(b) = 1/2*[sin(a b) sin(a-b)]
cos(a)sin(b) = 1/2*[sin(a b)-sin(a-b)]
诱导公式
sin(-a) = -sin(a)
cos(-a) = cos(a)
sin(π/2-a) = cos(a)
cos(π/2-a) = sin(a)
sin(π/2 a) = cos(a)
cos(π/2 a) = -sin(a)
sin(π-a) = sin(a)
cos(π-a) = -cos(a)
sin(π a) = -sin(a)
cos(π a) = -cos(a)
tgA=tanA = sinA/cosA
万能公式
sin(a) = [2tan(a/2)] / {1 [tan(a/2)]²}
cos(a) = {1-[tan(a/2)]^2} / {1 [tan(a/2)]²}
tan(a) = [2tan(a/2)]/{1-[tan(a/2)]^2