初中三角公式大全（三角公式大全）

大家好，我是小十，我来为大家解答以上问题。初中三角公式大全，三角公式大全很多人还不知道，现在让我们一起来看看吧！

两角和公式 sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB tan(A+B)=(tanA+tanB)/(1-tanAtanB) tan(A-B)=(tanA-tanB)/(1+tanAtanB) ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA) ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA) 倍角公式 tan2A=2tanA/(1-tan2A) ctg2A=(ctg2A-1)/2ctga cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a 半角公式 sin(A/2)=√((1-cosA)/2) sin(A/2)=-√((1-cosA)/2) cos(A/2)=√((1+cosA)/2) cos(A/2)=-√((1+cosA)/2) tan(A/2)=√((1-cosA)/((1+cosA)) tan(A/2)=-√((1-cosA)/((1+cosA)) ctg(A/2)=√((1+cosA)/((1-cosA)) ctg(A/2)=-√((1+cosA)/((1-cosA)) 和差化积 2sinAcosB=sin(A+B)+sin(A-B) 2cosAsinB=sin(A+B)-sin(A-B) 2cosAcosB=cos(A+B)-sin(A-B) -2sinAsinB=cos(A+B)-cos(A-B) sinA+sinB=2sin((A+B)/2)cos((A-B)/2 cosA+cosB=2cos((A+B)/2)sin((A-B)/2) tanA+tanB=sin(A+B)/cosAcosB tanA-tanB=sin(A-B)/cosAcosB ctgA+ctgBsin(A+B)/sinAsinB -ctgA+ctgBsin(A+B)/sinAsinB

1.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)

2.两角和与差的三角函数

sin(a + b) = sin(a)cos(b) + cos(α)sin(b) cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b) cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a + b) = [tan(a) + tan(b)] / [1 - tan(a)tan(b)]

tan(a - b) = [tan(a) - tan(b)] / [1 + tan(a)tan(b)]

3.和差化积公式 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]

4.积化和差公式

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)]

5.二倍角公式 sin(2a) = 2sin(a)cos(b)

cos(2a) = cos2(a) - sin2(a) = 2cos2(a) -1=1 - 2sin2(a)

6.半角公式 sin2(a/2) = [1 - cos(a)] / 2

cos2(a/2) = [1 + cos(a)] / 2

tan(a/2) = [1 - cos(a)] /sin(a) = sina / [1 + cos(a)]

7.万能公式 sin(a) = 2tan(a/2) / [1+tan2(a/2)]

cos(a) = [1-tan2(a/2)] / [1+tan2(a/2)]

tan(a) = 2tan(a/2) / [1-tan2(a/2)]

本文到此讲解完毕了，希望对大家有帮助。

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