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 evenfunction 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:

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: Some Old Hippie, Caught Another Hippie, Tripping On Acid (awaiting approval from Mr. Geocaris)

## Odd/Even Functions

## Odd Functions include sine, cosecant, tangent, and cotangent.

## Odd functions are characterized by having different end behavior.

## A function

–fis said to be anoddfunction if for any numberx,f(–x)f(x). A functionfis said to be anevenfunction if for any numberx,f(–x) =f(x).=## Sine is an odd function, and cosine is even

## sin –

–sintt,and = cos –t= cost.These facts follow from the symmetry of the unit circle across the

x-axis. The angle –tis the same angle astexcept it's on the other side of thex-axis. Flipping a point (x,y) to the other side of thex-axis makes it into (x,–y), so they-coordinate is negated, that is, the sine is negated, but thex-coordinate remains the same, that is, the cosine is unchanged.Here are examples:## 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: SomeOldHippie,CaughtAnotherHippie,TrippingOnAcid (awaiting approval from Mr. Geocaris)