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?

Answer 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