Find the exact value of the slope of the line which is tangent to the curve given by the equation r = 2 + cos θ at theta equals pi over 2 . You must show your work.

Question

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

r = 2 + cos θ at  . You must show your work.

Answer 1

x=2 cos θ + cos²θ

y=2 sin θ + sin θ cos θ

dx/dθ = 2 sin θ (1+cos θ)

dy/dt = 2cos θ + cos 2θ

dy/dx = (dy/dt)/(dx/dt) ....you can write that out for yourself

At π/2

x=0, y=2 and dy/dx = 1/2

The tangent is 1/2 = (y-2)/x, i.e. y = (x/2)+2.

I graphed it on my graphing utility and it looked pretty good!

P.S.

I never did this before...so tutors learn things too!

P.P.S.

Just in case you should need it, the polar form of the tangent line is:

r=2/(sin θ-.5 cos θ)