三角函数公式大全包括？
1.诱导公式sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(π2-a)=cos(a)
cos(π2-a)=sin(a)
sin(π2+a)=cos(a)
cos(π2+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=sinAcosA
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+b2)cos(a-b2)
sin(a)−sin(b)=2cos(a+b2)sin(a-b2)
cos(a)+cos(b)=2cos(a+b2)cos(a-b2)
cos(a)-cos(b)=-2sin(a+b2)sin(a-b2)
4.积化和差公式
(上面公式反过来就得到了)
sin(a)sin(b)=-12⋅[cos(a+b)-cos(a-b)]
cos(a)cos(b)=12⋅[cos(a+b)+cos(a-b)]
sin(a)cos(b)=12⋅[sin(a+b)+sin(a-b)]
5.二倍角公式
sin(2a)=2sin(a)cos(a)
cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)
6.半角公式
sin2(a2)=1-cos(a)2
cos2(a2)=1+cos(a)2
tan(a2)=1-cos(a)sin(a)=sina1+cos(a)
7.万能公式
sin(a)=2tan(a2)1+tan2(a2)
cos(a)=1-tan2(a2)1+tan2(a2)
tan(a)=2tan(a2)1-tan2(a2)
8.其它公式(推导出来的
)
a⋅sin(a)+b⋅cos(a)=a2+b2sin(a+c)
其中
tan(c)=ba
a⋅sin(a)-b⋅cos(a)=a2+b2cos(a-c)
其中
tan(c)=ab
1+sin(a)=(sin(a2)+cos(a2))2
1-sin(a)=(sin(a2)-cos(a2))2
其他非重点
csc(a)=1sin(a)
sec(a)=1cos(a)
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绛旓細sin(-伪)= -sin伪锛沜os(-伪) = cos伪锛泂in(蟺/2-伪)= cos伪锛沜os(蟺/2-伪) =sin伪锛sin(蟺/2+伪) = cos伪锛沜os(蟺/2+伪)= -sin伪锛泂in(蟺-伪) =sin伪锛沜os(蟺-伪) = -cos伪锛泂in(蟺+伪)= -sin伪锛沜os(蟺+伪) =-cos伪锛泃anA= sinA/cosA锛泃an锛埾/2锛嬑憋級锛濓紞c...
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绛旓細涓銆乻in搴︽暟鍏紡 1銆乻in 30= 1/2 2銆乻in 45=鏍瑰彿2/2 3銆乻in 60= 鏍瑰彿3/2 浜屻乧os搴︽暟鍏紡 1銆乧os 30=鏍瑰彿3/2 2銆乧os 45=鏍瑰彿2/2 3銆乧os 60=1/2涓夈乼an搴︽暟鍏紡 1銆乼an 30=鏍瑰彿3/3 2銆乼an 45=1 3銆乼an 60=鏍瑰彿3
