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).

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°

=
3
2
cos20°+
1
2
sin20°−sin20°
1
2
cos20°−
3
2
sin20°−cos20°

=
3
2
cos20°−
1
2
sin20°
1
2
cos20°−
3
2
sin20°

=
sin120°cos20°+cos120°sin20°
cos120°cos20°−sin120°sin20°

=
sin140°
cos140°

=tan140°.
故答案为140°.