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正弦余弦公式

正弦余弦公式

cos1=0.54030230586814      sin1=0.8414709848079cos0=1                     sin0=0cos30°=√3/2             sin30°=1/2cos45°=√2/2            sin45°=√2/2cos60°=1/2             sin60°=√3/2 cos来自90°=0                sin90°=1cos12360问答0°=-1/2           sin120°=√3/2 cos135°=-√2/2         sin135°=√2/2cos150°=-√3/2         sin150°=1/2cos180°=-1              sin180°=0 co宣现高占单另延因草营金s210°=-√3/2         sin刑指要210°=-1/2cos225°=-√2/2         sin225°=-√2/2cos240°=-1/2            sin240°=-√3/2cos270°=赵曾诗推0               sin270°=-1cos300°=1/2            sin300°=-√3/2 cos315°=√2/毫脱协导础岩假们2          sin315°=-√2/2cos330°==√3/2         sin330°=-1/2cos360°=1               sin360°=0 诱导公式

sin(-a)=-sin(a)

cos(-a)=cos(a)

sin(π/离知粒威征目击按属神2-a)=cos(a)

cos(π/2-a)=sin(a)

sin(π/2+a)=cos(a)

co审温s(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 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石想置使革感货导-b)=sin(a)cos(b)-cos(息养冷含原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))

ta虽财脱石章司铁毫汽深置n(a-b)=(tan(a)-tan(b))/(1+tan(a)tan(b)) 三角函数和差化积公式

sin(a)+sin(b)=2sin((a+b)/2)cos((a-b)/2)

sin(a)−sin(b)=2cos建((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)

积化和差公式

sin(a)sin(b)=春来医大审-1/2*[cos(a+b)-cos(a-b)]

cos(a)co朝三何很事兰硫容令s(b)=1/2*[c师末振黑列我即能os(a+b)+cos(a-b)]

sin(a)cos(b)=1/2*[sin(见a+b)+sin(a-b)]

二倍角公式

sin(2a)=2sin(a)c安发次色os(a)

cos(2a)=cos^2(a)-sin^2(a)=2cos^2(a)-1=1-2sin^2(a)

半角公式

sin^煤2(a/2)=(1-cos(a))/2

cos^2(a/2)=(1+cos(a))/2

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

万能公式

sin(a)=(2tan(a/2))/(1+tan^2(a/2))

cos(a)=(1-tan^2(a/2))/(1+tan^2(a/2))

tan(a)=(2tan(a/2))/(1-tan^2(a/2))

其它公式

a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c)[其中,tan(c)=b/a]

a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c)[其中,tan(c)=a/b]

1+sin(a)=(sin(a/2)+cos(a/2))^2

1-sin(a)=(sin(a/2)-cos(a/2))^2

其他非重点三角函数

csc(a)=1/sin(a)

sec(a)=1/cos(a)

双曲函数

sinh(a)=(e^a-e^(-a))/2

cosh(a)=(e^a+e^(-a))/2

tgh(a)=sinh(a)/cosh(a)