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.

Here are examples:

external image Even-Odd-Identities.jpg

Even Functions are cosine and secant. These have the same end behavior.

Below is an example of each


external image trigo_functions.gif SinCos.gif

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

Figure 15 is an example of Tangent and Cotangent.

external image f66.jpg

Hint: SOH - CAH - TOA

Hint #2: Some Old Hippie, Caught Another Hippie, Tripping On Acid (awaiting approval from Mr. Geocaris)
external image Image3125.gif
external image triangle-soh-cah-toa.png