Problem 9. (5 pts each) (i) Find the Maclaurin series for sine and prove that it represents sinr for all re R. (1i) Deduce the power series expansion (centered at () for cosr, for every r E R. (iii) Find the first three nonzero terms in the power series representation (centered at () for tan r. tanc - T (iv) Use Part (iii) to evaluate lim Problem 10. Let r be a positive real number. (a) (4 pts) Find the tangent to the cycloid r = r(0 - sin0), y = r(1 - cos0) at the point 0 = 4/3. (b) (3 pts each) At what points is the tangent horizontal? When is it vertical