Even+and+Odd+Functions

=Odd/Even Functions= = Odd Functions include sine, cosecant, tangent, and cotangent. = = Odd functions are characterized by having different end behavior. = = = =A function //f// is said to be an // odd // function if for any number //x,// //f//( – //x//)= – //f//(//x//). A function //f// is said to be an // even // function if for any number //x,// //f//( – //x//) = //f//(//x//).= =Sine is an odd function, and cosine is even= = = = sin –//t// = –sin //t,// and = cos –//t// = cos //t.// These facts follow from the symmetry of the unit circle across the //x//-axis. The angle –//t// is the same angle as //t// except it's on the other side of the //x//-axis. Flipping a point (//x,y//) to the other side of the //x//-axis makes it into (//x,–y//), so the //y//-coordinate is negated, that is, the sine is negated, but the //x//-coordinate remains the same, that is, the cosine is unchanged.

[[image:http://www.math-coaching.com/images/Even-Odd-Identities.jpg width="148" height="247"]]
=Even Functions are cosine and secant. These have the same end behavior.=

= Below is an example of each =



= = = = = = =Odd Functions are sine, cosecant, tangent and cotangent. These have different end behavior.=

= Figure 15 is an example of Tangent and Cotangent. =



Hint: SOH - CAH - TOA
**Hint #2: S**ome **O**ld **H**ippie, **C**aught **A**nother **H**ippie, **T**ripping **O**n **A**cid (awaiting approval from Mr. Geocaris) = = =media type="youtube" key="LzSZFBHYVb4" width="425" height="350"= =media type="youtube" key="Aw8OszkQFVA" height="385" width="480"= media type="youtube" key="v2ni9bwO4v4" height="385" width="480"