Trigonometry Series (Part 4)

Today we look at several formulas which tend to be helpful when we are solving trigonometric equations or working with specific angles. They are also useful for simplifying expressions.

Addition formulas:


The formula for tan can be derived by making use of the formulas for sin and cos.


Subtraction formulas:

 
The subtraction formulas can be easily derived from the addition formulas by making use of the angle identities in Part 3.

Double-angle formulas:


These formulas can be derived from the addition formulas by letting y=x and using some identities.

Half-angle formulas:



These formulas can be obtained by rewriting the double-angle formulas.

Next time we will consider a few problems and examples, showing how we can apply and use all the information that we have from the previous parts in the series.