Saturday, 4 March 2017

Trigonometric Proofs

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. 

How would you work out this question using the rule above?

You could break this down into cos(60 - 45), and put these numbers into the formula.

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