Find the slope of the line tangent to the curve rcos2 theta

Solution

r = cos(2 + 1), r\' = dr/d = -2sin(2 + 1)

y = rsin, dy = dr sin + rcos d = (r\'sin + rcos) d = [-2sin(2 + 1) sin + cos(2 + 1) cos] d

x = rcos, dx = dr cos - rsin d = (r\'cos - rsin) d = [-2sin(2 + 1) cos - cos(2 + 1) sin]d

so sy/dx = [2sin(2 + 1) sin - cos(2 + 1) cos]/[2sin(2 + 1) cos + cos(2 + 1) sin]