Trig Functon

Period of Pi

Goes to -1 and back when x = pi

Amplitude of one

Graph has max and min of one

It has a max value of 1 and min of -1 on unit circle

Same as sin(x)

Modifying phase shift can give us the Y coordinate or the graph of sin(x)

Same period

X goes to 1 the same as y goes to one

Same rate

One depends on other

Both make up the angle

When one decreases the other increases then vice versa when they hit the midpoint

Repeats itself every 2 times pi

One revolution around the unit circle

Represented by y=cos(x)

Same x coordinate when the phase shift is done

Same properties

Same amplitude

Same zeros

when phase shift is modified by pi over 2

Same Period

RRead "same Period"

Same amp

Sin(x) and cos(x) both approach 1 and -1

Can be shown in graph

Because of radius

When the value exceeds 1 and neg 1

Divide by radius

Figure out domain and modify

Is the X-Axis on the unit circle

arccos(x)

Inverse function

Backwards

Domain

Switches with range

Reverse machine

Range

Switches with domain

Reverse machine

Reverses whas cos(x) does

Can delete cos(x) in algebra

Just like logs

Handy in algebra

Just like exponents

Handy in algebra

Period of Pi

Same as Cos(x)

Both go to 1 and -1

Y coordinate returns to zero

Amplitude of 1

Sin(x) can only have a maximum value of 1

If it is over 1 then you divide by radius

The unit circle radius is one

Is the Y-Axis on the Unit Circle

Because of relation to right triangle

Direct relationships with angles and Y coordinate

Sin(x) = Opposite (Y) over Hypontenuse (Radius)

Represents the Y coordinate when the triangle is graphed

Is a function of X because based on what x is sin(x) follows with a Y coordinate.

That's how you graph it

Can be modified with phase shift to equal cos(x)

It looks like cos(x) when graphed

Same amplitude because of the unit circle with radius of 1

Same max's and min's

Same Zeros

When modified by pi over two

Inverse is arcsin(x)

Is used to remove sin(x) functions

It reverses the function that is being applied to X

Very Handy in Algebra equations

It works like Logorithms

Gives us the y value and we have to find the angle measure

Its usually a friendly angle

Can be used to model various events that repeat themselves

Seasons

How the planets cycle

Tides

Period of 2 Pi

Because it deals with two seperate varibles

Ratio between two

Is the x over the y points on the unit circle

Graph

Zeros

Its zeros are when sin equals 0

sin(x) over cos(x)

Sin(x) controls zero

Except when cos(x) equals zero

Asymptotes

When cos(x) equals zero

Happens at pi over two and 3pi over two

Gives undefined value

Non existent

You cannot divide by zero

arc tan(x)

Oppostite

Graph is reflected over x

Handy in algebra

Deletes tan(x)

Range

Switches with Domain

Domain

Have to be careful

Have to visualize unit circle

Confusing

Sends you to another spot on the unit circle