The graphs of the tangent, cotangent, secant, and cosecant functions have _______ asymptotes

Vertical

The tangent, cotangent, and cosecant functions are _______, so the graphs of these functions have symmetry with respect to the ____________.

Odd, origin

To sketch the graph of a secant or cosecant function, first make a sect of its ______________ function.

Reciprocal

For the function f(X)=g(X)*sinx, g(X) is called the ______ factor of the function f(X)

Dampening

The period of y=tanx is ____

Pi

The domain of y=Cotx is all real numbers such that _________

X does not equal npi where n is any integer

The range of y=secx is ______

(-infinity, -1]u[1, infinity)

The period of y=cscx is _______

2pi

When you plug trig functions into your calculator, make sure you are in the right ____

Mode (radian/degree)

The critical values of secant and cosine functions are the (same/opposite)

Same

If cosine=0, secant= ______, meaning those points are now _______

Undefined, asymptotes

What is one period of a secant or cosecant function

3 asymptotes and 1 U going up and 1 U going down

What is one period of a cotangent or tangent function

Asymptote to asymptote with one intercept between and two “amplitudes”

What is the period of a tangent and cotangent function

How does this differ from other functions

Pi/b

Other functions are 2pi/b

The tangent looks like a ____ function while the cotangent graph looks like a negative ____ function

Cubic, cubic

Initial critical value

Tangent:

Cotangent:

Intercept, asymptote

If an even graph is shifted, it has (symmetry/no symmetry)

No symmetry

Even graphs are:

Odd graphs are:

Cosecant, secant

Tangent, cotangent

How do you prove that a graph is odd algebraically?

Even?

Odd: plug in -X, you get -f(X)

Even: plug in -X, you get f(X)

One period of a sine or cosine function is called one _________ of the sine or cosine curve

Cycle

The ________ of a sine or cosine curve represents half the distance between the maximum and the minimum values of the function

Amplitude

For the function y=asin(bx-c), c/b represents the _______ _____ of the graph of the function

Phase shift

For the function y=d+acos(bx-c), d represents a ______ ________ of the graph of the function

Vertical shift