Has anyone attempted to validate the Hawkindale Angle formulas?

I have attempted to use them for obtaining irregular hip and valley angles and have found that they didn't work for me.In my first attempt I used 7/12 (30.25°) and 12/12 (45°). DD+D = 60.50° not 90°. SS and S were correct. I then used 8/12 (33.69° and 10/12 (39.8°), DD+D=90° however in this case SS was 61.92° and S was 23.11°.

The formula R1, hip or valley pitch angle, is Arctan(TanS x Sin D). That is incorrect it should be Arctan(TanS x CosineD),that formula is shown as the formula A7 for the plumb backing angle for a hip or valley.

I would be interested to know if anyone else has experienced difficulties with these formulas and how and if they have reformulated them.