若点(cosθ,sinθ)到直线χsinθ+ycosθ-1=0(0≤θ≤π/2)的距离是1/2,则θ的值为?有点搞不懂题目意思囧rz
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 12:32:18
![若点(cosθ,sinθ)到直线χsinθ+ycosθ-1=0(0≤θ≤π/2)的距离是1/2,则θ的值为?有点搞不懂题目意思囧rz](/uploads/image/z/3600369-9-9.jpg?t=%E8%8B%A5%E7%82%B9%EF%BC%88cos%CE%B8%2Csin%CE%B8%EF%BC%89%E5%88%B0%E7%9B%B4%E7%BA%BF%CF%87sin%CE%B8%2Bycos%CE%B8-1%3D0%EF%BC%880%E2%89%A4%CE%B8%E2%89%A4%CF%80%EF%BC%8F2%EF%BC%89%E7%9A%84%E8%B7%9D%E7%A6%BB%E6%98%AF1%EF%BC%8F2%2C%E5%88%99%CE%B8%E7%9A%84%E5%80%BC%E4%B8%BA%3F%E6%9C%89%E7%82%B9%E6%90%9E%E4%B8%8D%E6%87%82%E9%A2%98%E7%9B%AE%E6%84%8F%E6%80%9D%E5%9B%A7rz)
若点(cosθ,sinθ)到直线χsinθ+ycosθ-1=0(0≤θ≤π/2)的距离是1/2,则θ的值为?有点搞不懂题目意思囧rz
若点(cosθ,sinθ)到直线χsinθ+ycosθ-1=0(0≤θ≤π/2)的距离是1/2,则θ的值为?
有点搞不懂题目意思囧rz
若点(cosθ,sinθ)到直线χsinθ+ycosθ-1=0(0≤θ≤π/2)的距离是1/2,则θ的值为?有点搞不懂题目意思囧rz
根据点到直线的距离公式:
| sinθcosθ + cosθsinθ - 1 | / 根号(sin^2θ+cos^2θ) = 1/2
| 2sinθcosθ - 1 | = 1/2
| sin2θ - 1 | = 1/2
∵0≤θ≤π/2,0≤2θ≤π
∴0≤sin2θ≤1
∴1-sin2θ=1/2
∴sin2θ=1/2
∴2θ = π/6,或5π/6
∴θ=π/12,或 5π/12
d=|cosθsinθ+sinθcosθ-1|/根号(sin^2θ+cos^θ)=0.5
即1-sin2θ=0.5; sin2θ=0.5, 又 0≤2θ≤π, 所以 2θ=π/6 或 5π/6
θ=π/12 或 5π/12
点(m, n)到直线ax + by + c = 0的距离是 d = |am + bn + c|/√(a^2 + b^2)
d = |cosθsinθ + sinθcosθ -1| /√[(sinθ)^2 + (cosθ)^2] = |2sinθcosθ -1| = |sin(2θ) - 1| = 1/2 (使用(sinθ)^2 + (cosθ)^2 = 1)
sin(2θ...
全部展开
点(m, n)到直线ax + by + c = 0的距离是 d = |am + bn + c|/√(a^2 + b^2)
d = |cosθsinθ + sinθcosθ -1| /√[(sinθ)^2 + (cosθ)^2] = |2sinθcosθ -1| = |sin(2θ) - 1| = 1/2 (使用(sinθ)^2 + (cosθ)^2 = 1)
sin(2θ) - 1 = 1/2 或sin(2θ) - 1 = -1/2
(1) sin(2θ) - 1 = 1/2, sin(2θ) = 3/2 > 1, 无解
(2) sin(2θ) - 1 = -1/2, sin(2θ) = 1/2, 2θ = π/6或2θ = 5π/6, θ = π/12 或θ = 5π/12
收起