Question

一次函数Y=kx+b的图像经过点P（1,－3）且与X轴交于点A,与y轴交于点B,已知sin∠PAO＝3/5,求此函数的解

Answer 1

因为一次函数经过P(1,-3)所以-3=k+b`````````(1)

函数直线与X轴交于A点,与Y轴交于B点,则A点的坐标为(-b/k,0),B点的坐标为(0,b)

画图可知,sin∠PAO=OB/AB=3/5````````````(2)

又因为OB=b,AB2=b2+(-b/k)2````````````````(3)

联合(1) (2) (3),得

k=3/4,b=-15/4或k=-3/4,b=-9/4