文档介绍:高中数学三角函数知识点总结
高三数学知识点总结
:锐角三角函数公式
sin =的对边 / 斜边
cos =的邻边 / 斜边
tan =的对边 / 的邻边
cot =的邻边 / 的对边
倍角公式
Sin2A=2SinA?CosA
Cos2A=CosA^2SinA^2=12SinA^2=2CosA^21
tan2A=2tanA/1tanA^2
注:SinA^2 是sinA的平方 sin2A
:三倍角公式
sin3=4sinsin/3+sin/3
cos3=4coscos/3+cos/3
tan3a = tan a tan/3+a tan/3a
:三倍角公式推导
sin3a
=sin2a+a
=sin2acosa+cos2asina
:辅助角公式
Asin+Bcos=A^2+B^2^1/2sin+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^2^1/2cost,tant=A/B降幂公式
sin^2=1cos2/2=versin2/2
cos^2=1+cos2/2=covers2/2
tan^2=1cos2/1+cos2
:推导公式
tan+cot=2/sin2
tancot=2cot2
1+cos2=2cos^2
1cos2=2sin^2
1+sin=sin/2+cos/2^2
=2sina1sin2a+12sin2asina
=3sina4sin3a
cos3a
=cos2a+a
=cos2acosasin2asina
=2cos2a1cosa21sin2acosa
=4cos3a3cosa
sin3a=3sina4sin3a
=4sina3/4sin2a
=4sina[3/22sin2a]
=4sinasin260sin2a
=4sinasin60+sinasin60sina
=4sina*2sin[60+a/2]cos[60a/2]*2sin[60a/2]cos[60a/2]
=4sinasin60+asin60a
cos3a=4cos3a3cosa
=4cosacos2a3/4
=4cosa[cos2a3/22]
=4cosacos2acos230
=4cosacosa+cos30cosacos30
=4cosa*2cos[a+30/2]cos[a30/2]*{2sin[a+30/2]sin[a30/2]}
=4cosasina+30sina30
=4cosasin[9060a]sin[90+60+a]
=4cosacos60a[cos60+a]
=4cosacos60acos60+a
上述两式相比可得
tan3a=tanatan60atan60+a
:半角公式
tanA/2=1cosA/sinA=sinA/1+cosA;
cotA/2=sinA/1cosA=1+cosA/sinA.
sin^2a/2=1cosa/2
cos^2a/2=1+cosa/2
tana/2=1cosa/sina=sina/1+cosa三角和
sin++=sincoscos+cossincos+coscossinsinsinsin
cos++=coscoscoscossinsinsincossinsinsincos
tan++=tan+tan+tantantantan/1tantantantantantan
:两角和差
cos+=coscossinsin
cos=coscos+sinsin
sin=sincoscossin
tan+=tan+tan/1tantan
tan=tantan/1+tantan
:和差化积
sin+sin = 2 sin[+/2] cos[/2]
sinsin = 2 cos[+/2] sin[/2]
cos+cos = 2 co