设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0
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![设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0](/uploads/image/z/12971258-26-8.jpg?t=%E8%AE%BE%E7%9B%B4%E7%BA%BFax%2Bby%2Bc%E7%9A%84%E5%80%BE%E8%A7%92%E4%B8%BAa%2Csina%2Bcosa%3D0%2C%E5%88%99a%2Cb%E6%BB%A1%E8%B6%B3%3Fa-b%3D0)
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设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0
设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0
设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0
sina+cosa=0,
tana+1=0
tana=-1=k
ax+by+c=0
by=-ax-c
y=-ax/b-c/b
斜率k=-a/b=-1
a=b
a-b=0
sina+cosa=0
sina=-cosa
tana=-1
k=-1
因此-a/b=k=-1
即a-b=0
sina+cosa=0
sina=-cosa
tana=-1
ax+by+c=0
y=-a/bx-c/b
所以tana=-1=-a/b
a/b=1
a=b
a-b=0
sina=-cosa
tana=sina/cosa=-1
倾斜角的正切就是斜率
ax+by+c=0
y=(-a/b)x-c/b
斜率k=-a/b=-1
a=b
a-b=0