在直角坐标平面内,已知点A(3,0)B(0,3)C(cosθ,sinθ),θ∈(π/2,3π/2)若向量丨AC丨=向量丨BC丨,求角θ的弧度数2.若向量AC*BC=-1,求2sin²θ-sin2θ/1+tanθ的值
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![在直角坐标平面内,已知点A(3,0)B(0,3)C(cosθ,sinθ),θ∈(π/2,3π/2)若向量丨AC丨=向量丨BC丨,求角θ的弧度数2.若向量AC*BC=-1,求2sin²θ-sin2θ/1+tanθ的值](/uploads/image/z/8441677-37-7.jpg?t=%E5%9C%A8%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E5%B9%B3%E9%9D%A2%E5%86%85%2C%E5%B7%B2%E7%9F%A5%E7%82%B9A%283%2C0%29B%280%2C3%29C%28cos%CE%B8%2Csin%CE%B8%29%2C%CE%B8%E2%88%88%EF%BC%88%CF%80%2F2%2C3%CF%80%2F2%EF%BC%89%E8%8B%A5%E5%90%91%E9%87%8F%E4%B8%A8AC%E4%B8%A8%3D%E5%90%91%E9%87%8F%E4%B8%A8BC%E4%B8%A8%2C%E6%B1%82%E8%A7%92%CE%B8%E7%9A%84%E5%BC%A7%E5%BA%A6%E6%95%B02.%E8%8B%A5%E5%90%91%E9%87%8FAC%2ABC%3D-1%2C%E6%B1%822sin%26sup2%3B%CE%B8-sin2%CE%B8%2F1%2Btan%CE%B8%E7%9A%84%E5%80%BC)
在直角坐标平面内,已知点A(3,0)B(0,3)C(cosθ,sinθ),θ∈(π/2,3π/2)若向量丨AC丨=向量丨BC丨,求角θ的弧度数2.若向量AC*BC=-1,求2sin²θ-sin2θ/1+tanθ的值
在直角坐标平面内,已知点A(3,0)B(0,3)C(cosθ,sinθ),θ∈(π/2,3π/2)若向量丨AC丨=向量丨BC丨,求角θ的弧度数
2.若向量AC*BC=-1,求2sin²θ-sin2θ/1+tanθ的值
在直角坐标平面内,已知点A(3,0)B(0,3)C(cosθ,sinθ),θ∈(π/2,3π/2)若向量丨AC丨=向量丨BC丨,求角θ的弧度数2.若向量AC*BC=-1,求2sin²θ-sin2θ/1+tanθ的值
1、向量AC=(cosθ-3,sinθ),
向量BC=(cosθ,sinθ-3),
|AC|=√[(cosθ-3)^2+(sinθ)^2]=√(10-6cosθ),
|BC|=√[(cosθ)^2+(sinθ-3)^2]=√(10-6sinθ),
10-6cosθ=10-6sinθ,
sinθ=cosθ,
tanθ=1,θ∈(π/2,3π/2)
θ=5π/4,
2、向量AC·BC=(cosθ)^2-3cosθ+(sinθ)^2-3sinθ
=1-3(sinθ+cosθ)=-1,
sinθ+cosθ=2/3>0,(1),θ∈(π/2,π),
对(1)式两边平方,
1+sin2θ=4/9,
sin2θ=-5/9,
(sinθ-cosθ)^2=1-sin2θ=1+5/9=14/9,
sinθ-cosθ=±√14/3,
sinθ>0,cosθ0,
第2象限应取正,
sinθ-cosθ=√14/3,(2)
不知道有无括号,我给你加上括号来做,
(2sin²θ-sin2θ)/(1+tanθ)
=2sinθ(sinθ-cosθ)cosθ/(sinθ+cosθ)
=sin2θ(sinθ-cosθ)/(sinθ+cosθ)
=(-5/9)(√14/3)/(2/3)
=-5√14/18.