Let T₀ : R² R² be reflection in the x-axis. Let T_i : R ² R ² be the reflection in the line y = tan(i/8)x for 1 i 3, and let T₄ : R ² R ² be reflection in the y-axis.

(a) Using Matlab, compute the matrices for T₀ and T_i for 1 i 4, and for the composition Ti T0.

(b) Use Matlab to list the matrices for rotating by angle i/4 for 1 i 4.

(c) Make a conjecture based on your data.

(d) Check this conjecture on an example of your own creation. Explicitly, choose a new line L, and let T 0 be reflection in this line. Check that the composition T 0 T0 is what is predicted by your conjecture. You may find the commands asin and acos useful here (type help asin to get the help page for these commands)