trigonometry

The sine function starts life in a triangle (year 9?) then becomes intimate with a circle at A level, as y-coord of a point rotating on a unit circle.  Later it is about infinite series or, even, differential equations.

Carr’s 626, in his magical book for Edwardian mathematical autodidacts, provides summary of general solutions for trigonometrical equations useful to STEP and A level students.

Friendly triangles – good visual method for memorising trig ratios of 30, 45 and 60 degree angles. Known for thousands of years as per the Babylonian tablet