Find the slope of the tangent line of the curve r theta eth

Solution

r = *e, r\' = dr/d = (1 + )e

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

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

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