Trigonometric Function (2) - 코사인 법칙, 합차, 곱셈 공식

8. 제1코사인 법칙

 

$ a=bcosC+ccosB $

$ b=ccosA+acosC $

$ c=acosB+bcosA $

 

9. 제2코사인 법칙

 

$ a^{2}=b^{2}+c^{2}-2bccosA $

$ b^{2}=a^{2}+c^{2}-2accosB $

$ c^{2}=a^{2}+b^{2}-2abcosC $

 

10. 합차공식

 

$ sin\alpha +sin\beta =2sin(\frac{\alpha +\beta }{2})cos(\frac{\alpha -\beta }{2}) $

$ sin\alpha -sin\beta =2cos(\frac{\alpha +\beta }{2})sin(\frac{\alpha -\beta }{2}) $

$ cos\alpha +cos\beta =2cos(\frac{\alpha +\beta }{2})cos(\frac{\alpha -\beta }{2}) $

$ cos\alpha -cos\beta =-2sin(\frac{\alpha +\beta }{2})sin(\frac{\alpha -\beta }{2}) $

 

11. 곱셈공식

 

$ sin\alpha cos\beta =\frac{1}{2}[sin(\alpha +\beta )+sin(\alpha -\beta )] $

$ cos\alpha sin\beta =\frac{1}{2}[sin(\alpha +\beta )-sin(\alpha -\beta )] $

$ cos\alpha cos\beta =\frac{1}{2}[cos(\alpha +\beta )+cos(\alpha -\beta )] $

$ sin\alpha sin\beta =-\frac{1}{2}[cos(\alpha +\beta )-cos(\alpha -\beta )] $