What is the slope of the polar curve #f(theta) = -theta + sectheta - costheta # at #theta = (5pi)/4#?
The reference Tangents to a polar curve gives us the following equation for
Compute the first derivative of equation :
Substitute equation  and equation  into equation :
Evaluate equation  at
Here is the equation of the tangent line:
Here is a graph of the curve, the point of tangency, and the tangent line: