I just need help getting Cn. Thanks!

(10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, 6,u(t, x) = 46u(t, x), t G (0, co), x E (0, 1); with initial condition 3, x e [0, 1), 14(0, x) = foe) = 1 2 0, x e [5, 1]. and with boundary conditions 6xu(t,0) = 0, u(t, 1) = 0. Find the solution :4 using the expansion 00 W. x) = 2 6.. vno') wn(x), n=l with the normalization conditions v,,(0) = 1, w,,(0) = 1. a. (3/10) Find the functions w,l , with index n 2 1. w,l = [cos((2n-1)(pi/2)x) 2 b. (3/10) Find the functions U", with index n 2 1. v,, = l eA(-4((2n1)(pi/2))A2*t) 2 c. (4/10) Find the coefficients c,\" with index n 2 1. c,, ' 4((2n1)*pD*cos(n*pi/2+pi/4) [ Z