A loxodrome, or rhumb line, L, may be parametrized by longitude, 0: rhumb (0) = sech (t.0). cos (8) sin (0) sinh (t - 0) „]-[ cos (0) sech (t0) sin (0) sech (t.0) tanh(t.0) (1) where t > 0 is a fixed parameter to identify the rhumb line among others. a).Find the magnitude [4, §12.2], rhumb (0)|, of the vector rhumb (0): rhumb (0)| = (2) (b) Find the derivative [4, §13.2], rhumb' (0), of the vector rhumb (0): rhumb' (0) = (3) (c) Find the magnitude [4, §12.2] of the derivative, |rhumb' (0)|: rhumb' (0)| (4) (d) The parallel at latitude X may be parametrized with longitude, 0, by p (0) = cos (0) cos (X) sin (0) · cos(x) sin (X) (5) Find the derivative [4, §13.2], p' (0), of p (0): p' (0) (6) = (e) Find the angle [4, §12.3], denoted here by 3, between the tangent to the parallel, p' (0), and the tangent to the rhumb line, rhumb' (0). (f) Find the following integral [4, §6.7]: , sech (z) dz = (7) (g) Find the arc length [4, §13.3] of the rhumb line L from 0 = − [infinity] to 0 = [infinity]0: 1 ds = (8)