For the wave equation of epsilon = epsilon(0) cos (wt -kx + phi), what would it be if the wave was?

Question

a, propagating in the negative x direction

b, out of phase by 90 degrees

Answer 1

a) change x to -x to get
ε = ε(0) cos (ωt + kx + φ)

b) change φ to φ + 90° to get
ε = ε(0) cos (ωt - kx + φ + 90°)
and use cos(t + 90°) = - sin t to get
= -ε(0) sin (ωt - kx + φ)