Find the equation of the tangent line to the curve at = /4. Explanation. We start by computing the derivative in rectangular coordinates. Recall that z(6) = (1 + 2sin(d)) - cos(f) = cos(#) + 2sin(f) cos(d) y(8) = (1 + 2sin(8)) - sin(8) = sin(8) + 2sin'(6) Consequently, 2(6) = H y(6) = [ and therefore dy sl B When 0 = w/4, z(0) = (14sqrt(2)/2) y(0) = (1+sart(2)/2) s @ dz Thus the equation of the line (in coordinates) tangent to the limacon at = /4 is