大师作文网已知α=1050°,化简sin(540°-α)/tan(α-180°)×sin(-α-360°)/cos(720°-α)
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/12 22:14:34
已知α=1050°,化简sin(540°-α)/tan(α-180°)×sin(-α-360°)/cos(720°-α)
sin(540°-α)/tan(α-180°)×sin(-α-360°)/cos(720°-α)
= sin(- 510°)/tan(870°)×sin(-1050°)/cos(- 1050°)
=sin(- 510°+720°)/tan(870°- 720°)×sin(-1050°+1080°)/cos(- 1050°+1080°)
=sin(210°)/tan(150°)×sin(30°)/cos(30°)
=- 1/2 ×(-√3) ×1/2 ×2/√3
=1/2
考查的是周期性,可以加减360度的任意整数倍
= sin(- 510°)/tan(870°)×sin(-1050°)/cos(- 1050°)
=sin(- 510°+720°)/tan(870°- 720°)×sin(-1050°+1080°)/cos(- 1050°+1080°)
=sin(210°)/tan(150°)×sin(30°)/cos(30°)
=- 1/2 ×(-√3) ×1/2 ×2/√3
=1/2
考查的是周期性,可以加减360度的任意整数倍
已知α=1050°,化简sin(540°-α)/tan(α-180°)×sin(-α-360°)/cos(720°-α)
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