Relationships Between Values of Trigonometric Functions

There are some very useful relationships between the values of the elementary trigonometric functions that rely on the symmetry of thise functions.

The functionis symmetrical in the lineand

This means that

also has rotational symmetry about the pointThis mean that

The functionis symmetrical in the line

This means that

also has rotational symmetry aboutandThis means thatand

has no lines of symmetry but has translational symmetry of period %pi and rotational symmetry in the pointsand This means thatand

All the trigonometric functions have translational symmetry of periodThis means that

In fact we also have the relationship between the sin and cosine functionsand

The above relationships can be generalised.

and

and

and

and