Parametrics (1 Viewer)

[Michaelmoo]

Find the Equation of the tangent and the normal for:

x=cos2t
y=cost

at the point t= pi/4

 

[Trebla]

dx/dt = -2sin 2t
dy/dt = -sin t
dy/dx = (dy/dt) / (dx/dt)
= sin t / 2sin 2t
At t = π/4
x = 0
y = 1 / √2
dy/dx = 1 / (2√2)
Gradient of tangent = 1 / (2√2)
Equation of tangent:
y - 1 / √2 = x / (2√2)
Gradient of normal = - 2√2
Equation of normal:
y - 1 / √2 = - 2√2 x