Trigonometrie lernen : Merkzettel

Trigonometrische Formeln

Hier sind die wichtigsten trigonometrischen Formeln, die zur Vereinfachung trigonometrischer Berechnungen verwendet werden können.

• `AA x in RR, k in ZZ`,
  • `cos(-x)= cos(x)`
  • `cos(x+2*k*pi)=cos(x)`
  • `cos(pi-x)=-cos(x)`
  • `cos(pi+x)=-cos(x)`
  • `cos(pi/2-x)=sin(x)`
  • `cos(pi/2+x)=-sin(x)`
• `AA x in RR, k in ZZ`,
  • `sin(-x)= -sin(x)`
  • `sin(x+2*k*pi)=sin(x)`
  • `sin(pi-x)=sin(x)`
  • `sin(pi+x)=-sin(x)`
  • `sin(pi/2-x)=cos(x)`
  • `sin(pi/2+x)=cos(x)`
• `AA x in RR, k in ZZ`,
  • `tan(-x)= -tan(x)`
  • `tan(x+k*pi)=tan(x)`
  • `tan(pi-x)=-tan(x)`
  • `tan(pi+x)=tan(x)`
  • `tan(pi/2-x)=1/tan(x)`
  • `tan(pi/2+x)=-1/tan(x)`

• `cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b)`
• `cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)`
• `sin(a-b)=sin(a)*cos(b)-cos(a)*sin(b)`
• `sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)`

• `cos(2a)=(cos(a))^2-(sin(a))^2`
• `sin(2a)=2*sin(a)*cos(a)`

• `(cos(a))^2=(1+cos(2a))/2`
• `(sin(a))^2=(1-cos(2a))/2`
• `(cos(a))^2+(sin(a))^2=1`