一、三角函数定义式
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s i n A = a / c sinA=a/c sinA=a/c
c o s A = b / c cosA=b/c cosA=b/c
t a n A = a / b tanA=a/b tanA=a/b
c o t A = b / a cotA=b/a cotA=b/a
s e c A = c / b secA=c/b secA=c/b
c s c A = c / a cscA=c/a cscA=c/a
二、同角三角函数基本关系
1.倒数关系
t a n A c o t A = 1 tanAcotA=1 tanAcotA=1
s i n A c s c A = 1 sinAcscA=1 sinAcscA=1
c o s A s e c A = 1 cosAsecA=1 cosAsecA=1
2.商的关系
s i n A / c o s A = t a n A = s e c A / c s c A = 1 / c o t A sinA/cosA=tanA=secA/cscA=1/cotA sinA/cosA=tanA=secA/cscA=1/cotA
3.平方关系
s i n 2 A + c o s 2 A = 1 sin^2A+cos^2A=1 sin2A+cos2A=1
三、三角函数的诱导公式
1.和差公式
s i n ( A + B ) = s i n A c o s B + c o s A s i n B sin(A+B) = sinAcosB+cosAsinB sin(A+B) = sinAcosB+cosAsinB
s i n ( A − B ) = s i n A c o s B − c o s A s i n B sin(A-B) = sinAcosB-cosAsinB sin(A−B) = sinAcosB−cosAsinB
c o s ( A + B ) = c o s A c o s B − s i n A s i n B cos(A+B) = cosAcosB-sinAsinB cos(A+B) = cosAcosB−sinAsinB
c o s ( A − B ) = c o s A c o s B + s i n A s i n B cos(A-B) = cosAcosB+sinAsinB cos(A−B) = cosAcosB+sinAsinB
t a n ( A + B ) = ( t a n A + t a n B ) / ( 1 − t a n B t a n A ) tan(A+B) =(tanA+tanB)/(1-tanBtanA) tan(A+B) =(tanA+tanB)/(1−tanBtanA)
t a n ( A − B ) = ( t a n A − t a n B ) / ( 1 + t a n B t a n A ) tan(A-B) =(tanA-tanB)/(1+tanBtanA) tan(A−B) =(tanA−tanB)/(1+tanBtanA)
c o t ( A + B ) = ( c o t A c o t B − 1 ) / ( c o t B + c o t A ) cot(A+B) =(cotAcotB-1)/(cotB+cotA) cot(A+B) =(cotAcotB−1)/(cotB+cotA)
c o t ( A − B ) = ( c o t A c o t B + 1 ) / ( c o t B − c o t A ) cot(A-B) =(cotAcotB+1)/(cotB-cotA) cot(A−B) =(cotAcotB+1)/(cotB−cotA)
2.倍角公式
t a n 2 A = 2 t a n A / ( 1 − t a n 2 A ) tan2A =2tanA/(1-tan^2A) tan2A =2tanA/(1−tan2A)
s i n 2 A = 2 s i n A • c o s A sin2A=2sinA•cosA sin2A=2sinA•cosA
c o s 2 A = c o s 2 A − s i n 2 A = 2 c o s 2 A − 1 = 1 − 2 s i n 2 A cos2A = cos^2A-sin^2A =2cos^2A-1=1-2sin^2A cos2A = cos2A−sin2A =2cos2A−1=1−2sin2A
3.半角公式
s i n 2 ( A / 2 ) = ( 1 − c o s A ) / 2 sin^2(A/2)=(1-cosA)/2 sin2(A/2)=(1−cosA)/2
c o s 2 ( A / 2 ) = ( 1 + c o s A ) / 2 cos^2(A/2)=(1+cosA)/2 cos2(A/2)=(1+cosA)/2
t a n 2 ( x / 2 ) = ( 1 − c o s A ) / ( 1 + c o s A ) tan^2(x/2)=(1-cosA)/(1+cosA) tan2(x/2)=(1−cosA)/(1+cosA)
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