Trigonometric identities are used to manipulate trig equations in certain ways. Here is a list of them:
The six basic trigonometric functions can be defined using a right triangle:
The six trig functions are sine, cosine, tangent, cosecant, secant, and cotangent. They are abbreviated by using the first three letters of their name (except for cosecant which uses ). They are defined as follows:
From the last section, it is easy to see that the following hold:
Another useful identity that isn't a reciprocal relation is that .
Using the Pythagorean Theorem on our triangle above, we know that . If we divide by we get which is just . Dividing by or instead produces two other similar identities. The Pythagorean Identities are listed below:
Angle Addition Identities
(Otherwise known as sum-to-product identities)
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