求曲线{x=sin2t y=cost在t=π/3相应点处的切线方程和法线方程
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x=sin2t
dx/dt = 2cos2t
y=cost
dy/dt = -sint
dy/友裂dx =(dy/dt)/(dx/dt) = -sint/(2cos2t)
dy/dx | t=π/3 = -sin(π/3)/(2cos(2π/3)) = -(√3/2)/[ 2(-1/2)] = √3/2
x|t=π/3 = sin(2π/3)=√3/2
y|t=π/3 = cos(π/3)=1/2
切线方程, t=π/3
y-1/2 =(√3/2)(x-√洞滑3/2)
法线方程好颤闭, t=π/3
y-1/2 =(-2/√3)(x-√3/2)
dx/dt = 2cos2t
y=cost
dy/dt = -sint
dy/友裂dx =(dy/dt)/(dx/dt) = -sint/(2cos2t)
dy/dx | t=π/3 = -sin(π/3)/(2cos(2π/3)) = -(√3/2)/[ 2(-1/2)] = √3/2
x|t=π/3 = sin(2π/3)=√3/2
y|t=π/3 = cos(π/3)=1/2
切线方程, t=π/3
y-1/2 =(√3/2)(x-√洞滑3/2)
法线方程好颤闭, t=π/3
y-1/2 =(-2/√3)(x-√3/2)
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