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 theta equals pi over 2 . You must show your work. (10 points) Please check if this is right. I put a lot of work into this please check!

x= 2 cos θ + cos^2 θ
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)
At π/2 x= 0, y= 2 and dy/dx = 1/2
The tangent is 1/2 = (y-2)/x
y = (x/2)+ 2
slope = 1/2

Answer 1

looks good!