Part 1: Malus's law
45°
I = I0 cos²(θ) = 0.500 (I0 = 1)
Input is horizontal linear polarization (red). The analyser axis (teal) passes the projection; transmitted intensity follows cos².
Part 2: Wave plate
90°
Input: 45° linear, Ex = 0.707, Ey = 0.707 eiδ
Axis ratio (minor/major) = 1.000
The traced curve is the polarization ellipse over one period. δ = 0° gives a line, 90° gives a circle, in between gives an ellipse.