设P(x,y)是角a终边上一点,|OP|=√(x^2+y^2)
sina=y/r cosa=x/r
sin²α＋cos²α=y^2/(x^2+y^2)+x^2/(x^2+y^2)=1用九年级的知识在直角三角形ABC中是∠A=90° ∠B=a BC^2=AC^2+AB^2sina=AC/BC sin^2a=AC^2/BC^2cosa=AB/BCcos^2a=AB^2/BC^2sin²α＋cos²α=AC^2/BC^2+AB^2/BC^2=1