Tangent, Horizontal and Vertical Lines at the Pole

[IntegrateMe]

Help me understand exactly what is going on here. I'll put up an attempt at my solution:

Find the tangent lines at the pole r = sin5o, [0,pi] (note: o represents theta)

Equation: dy/dx = [f'(o)sino + f(o)coso]/[f'(o)coso - f(o)sino]

f(o) = sin5o
f'(o) = 5cos5o

plugging everything in we eventuate at:

dy/dx = [5*sino*coso + coso*sin5o]/[5cos5o*coso - sin5o*sino]

I'm stuck at this point. Any clue as to how i can advance?

 

[Mark44]

Help me understand exactly what is going on here. I'll put up an attempt at my solution:

Find the tangent lines at the pole r = sin5o, [0,pi] (note: o represents theta)

Equation: dy/dx = [f'(o)sino + f(o)coso]/[f'(o)coso - f(o)sino]

f(o) = sin5o
f'(o) = 5cos5o

plugging everything in we eventuate at:

dy/dx = [5*sino*coso + coso*sin5o]/[5cos5o*coso - sin5o*sino]

I'm stuck at this point. Any clue as to how i can advance?

You have a mistake in the numerator below. What is f'(o)sin(o)?
dy/dx = [5*sino*coso + coso*sin5o]/[5cos5o*coso - sin5o*sino]

For which values of theta is sin(5*theta) = 0? Evaluate your derivative function at those places.