已知:点A(cos80°,sin80°),B(cos20°,sin20°)则过A、B两点直线的倾斜角为 _°(用度回答).
问题描述:
已知:点A(cos80°,sin80°),B(cos20°,sin20°)则过A、B两点直线的倾斜角为 ______°(用度回答).
答
过A、B两点直线的斜率k=
sin80°−sin20° cos80°−cos20°
=
sin(60°+20°)−sin20° cos(60°+20°)−cos20°
=
sin60°cos20°+cos60°sin20°−sin20° cos60°cos20°−sin60°sin20°−cos20°
=
cos20°+
3
2
sin20°−sin20°1 2
cos20°−1 2
sin20°−cos20°
3
2
=
cos20°−
3
2
sin20°1 2 −
cos20°−1 2
sin20°
3
2
=
sin120°cos20°+cos120°sin20° cos120°cos20°−sin120°sin20°
=
sin140° cos140°
=tan140°.
故答案为140°.