Question

Find the exact value of the slope of the line which is tangent to the curve given by the equation

r = 1 - 2cos θ at theta equals pi over 2 .

Thank you in advance!

Answer 1

-2

Explanation:

x = r cos θ

y = r sin θ

dx/dθ = -r sin θ + r' cos θ

dy/dθ = r cos θ + r' sin θ

dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)

At θ = π/2, cos θ = 0, sin θ = 1, and r = 1. So the derivative simplifies to:

dy/dx = (r') / (-1)

dy/dx = -r'

dy/dx = -2 sin θ

dy/dx = -2