Additional Trigonometric Identities

There are several additional trigonometric identities which we want to highlight before moving on to applications of these identities.

First, we note the following two identities involving and which follow from the symmetries displayed by the graphs of these functions. They are:

These identities now allow us to determine the and of any negative angle in terms of the related absolute value. Hence, we no longer need to ``remember'' any trig values for negative angles. So, for example,

and

That should simplify some of our work tremendously.

Next, we want to look at a class of identities known as the sum and difference formulas. They are as follows:

These are so named because they give us ways to deal with trig values for sums of angles based on the two angles x and y in question. This will prove to be very useful in the examples we give below.

There are many related identities that are direct corollaries of the sum and difference formulas mentioned above. We mention some of these here. The following are known as the double-angle formulas:

The above are obtained by letting x=A and y=A in the sum formulas previously mentioned.

Next, we mention another set of formulas which are again by-products of the sum formulas mentioned above. They are known as the product-to-sum formulas:

Finally we mention the half-angle formulas:

This is in no way an exhaustive list of the known identities involving trigonometric functions. However, they provide a good foundation or starting point for you in terms of the identities you should know.