Identity: An equation which is true regardless of what values are substituted for any variables.
Identities apply to basic algebra as well as trigonometry, and especially to what we are learning. Identities apply to sin, cos, and tan. Because they each have a reciprocal we have learned about( csc, sec, and cot), its quite simple!
These are reciprocal identities. There are also Quotient Identities. These are derived from the 3 basic trigonometric functions, using substitution based on their definitions:
and
Finally, in class Mr. Wilhelm helped us derive the 1st of 3 Pythagorean Identities, using the Pythagorean Theorem, and using substitution by definitions:
Becomes...
To solve an identity, you must change and work with one side without altering the other. As Mr. Wilhelm told us, it is best to work with the crazy messy side and try to work towards the nice clean one. Lots of substituting!
Soo thats basically it i think, except for :
Please Mr. Wilhelm, I've never seen it and I think to fully enjoy it we need to be all together in class as to create the right atmosphere. :)
Good luck!
~Kendall
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