What is the slope of the polar curve f(theta) = theta + cottheta+thetasin^2theta at theta = (3pi)/8?

2 Answers
Jul 5, 2016

=1.51

Explanation:

  • The slope of any curve/function at a certain point is always the function's first derivative.
    Hence, the slope of f(theta)=f'(theta)
  • f'(theta)=1-csc^2theta+theta*2sintheta*costheta+sin^2theta
    =1-csc^2theta+thetasin2theta+sin^2theta
  • Therefore, the slope at theta=(3pi)/8 is
    f'((3pi)/8)=1-csc^2((3pi)/8)+(3pi)/8sin2((3pi)/8)+sin^2((3pi)/8)
    =1-1.17+0.83+0.85
    =1.51
Jul 5, 2016

Added graph

Explanation:

The graphing package I am using must have a slight error in the coding as the point does not sit exactly on the plotted line.
However; the uploaded image should give you a rough guide.

enter image source here