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Give the equation of the tangent line to the curve at given point x(t)=2 cos(t) y=2 sin(t) at t=pi/6?

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  1. x = 2cos t
    y = 2sin t

    dx/dt = -2sin t
    dy/dt = 2cos t

    slope = dy/dx
    = (dy/dt) / )dx/dt)
    = 2cost/-2sint
    = -cost/sint

    when t = pi/6
    sint = 1/2
    cost= √3/2
    slope = (-√3/2)/(1/2) = -√3

    point: (2cos pi/6, 2sin pi/6)
    or (√3 , 1)

    So now you have m = -√3, and the point (√3,1)

    equation of tangent:
    y - 1 = √3(x - √3)
    y - 1 = √3x - 3
    or
    y = √3x - 2

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