Lesson 8

What is tangent?

tan x = sinx/ cosx

When is tangent undefined?

When cos x = 0, at x = pi/2 + kpi. These are vertical asymptotes

Parent tangent T- table

Tangent’s period

pi

Why is tan(wx)’s period pi/w

Tangent’s parent graph repeats every pi, and the inside wx travels w times as fast. Solve wx = pi: x = pi/w

What is cotangent

cot x = cos x/sin x

When is cotangent undefined

When sin x =o, at x = kpi. There are vertical asympototes

Parent cotangent t-table

Cotangent’s parent period?

pi

Tangent vs. cotangent direction

Parent tangent rises left to right. Parent cotangent falls left to right.

How does A affect tangent/cotangent?

A > 0: keep the parent direction. A < 0 reflect vertically, so reverse the direction

In A tan(w(x-h)) + B what affects x-values?

The inside.

w changes period

h shifts horizontally

In A tan(w(x-h)) + B what affects y-values?

The outside

A is amplitude

B is vertical shifts

T-table x change order

divide parent x values by w, then add h

T- table y change order

multiply parent y values by A, then B. DNE stays DNE

What is secant?

sec x = 1/cosx

Parent secant t-table

Where is secant undefined?

Where cosine is 0: x = pi/2 + kpi

What is cosecant?

csc x = 1/sinx

Parent cosecant t-table

When is cosecant undefined?

Where sine is 0: x = kpi

What is the period of secant/cosecant

2pi/w

Can secant/cosecant cross y = B

NAUR!

Which ones are even

Sec x

Which ones are odd

tan x, cot x, and csc x