Question

Determine dy/dx in terms of t and evaluate it at the given value of t for the following parametric curves.a. x = 3 sin t, y = 2 cos t; t = pi/4b. x = 3t, y = 2t^3 ; t = 1Do you just do dx/dtheta then dy/dtheta and divide dy/dtheta by dx/dtheta? Then plug in value?

Answer 1

Step-by-step explanation:

You are correct.  dy/dx = (dy/dt) / (dx/dt)

x = 3 sin t

dx/dt = 3 cos t

y = 2 cos t

dy/dt = -2 sin t

dy/dx = (-2 sin t) / (3 cos t)

dy/dx = -⅔ tan t

t = π/4

dy/dx = -⅔ tan(π/4)

dy/dx = -⅔