#### Fundamental Law of Trigonometry

Let us assume that α > β > 0.

Consider a unit circle with centre O.

Let the terminal side of angles α and β
cut the unit circle at A and B respectively.

Evidently AOB = α - β.

Take a point C
on the unit circle so that XOC = AOB = α - β.

Join A with B and C with D.

The coordinates of A are ( cos α , sin α ).

The coordinates of B are ( cos β , sin β ).

The coordinates of C are [ cos(α - β) , sin(α - β) ].

The coordinates of D are ( 1 , 0 ) Now AOB and COD are congruent.

## No comments:

## Post a Comment