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Unit 2-Functions

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Tan(x)

arc tan(x)

Deletes tan(x)

Have to be careful

Sends you to another spot on the unit circle

Confusing

Have to visualize unit circle

Switches with Domain

Oppostite

Graph is reflected over x

Graph

Asymptotes

Gives undefined value

You cannot divide by zero

Non existent

When cos(x) equals zero

Happens at pi over two and 3pi over two

Zeros

sin(x) over cos(x)

Sin(x) controls zero

Except when cos(x) equals zero

Its zeros are when sin equals 0

Is the x over the y points on the unit circle

Period of 2 Pi

Because it deals with two seperate varibles

Ratio between two

Sin(x)

Can be used to model various events that repeat themselves

Tides

How the planets cycle

Seasons

Inverse is arcsin(x)

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

Its usually a friendly angle

Is used to remove sin(x) functions

It works like Logorithms

Very Handy in Algebra equations

It reverses the function that is being applied to X

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

When modified by pi over two

It looks like cos(x) when graphed

Same Zeros

Same max's and min's

Same amplitude because of the unit circle with radius of 1

Is the Y-Axis on the Unit Circle

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

That's how you graph it

Because of relation to right triangle

Represents the Y coordinate when the triangle is graphed

Direct relationships with angles and Y coordinate

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

Amplitude of 1

The unit circle radius is one

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

If it is over 1 then you divide by radius

Y coordinate returns to zero

Same as Cos(x)

Both go to 1 and -1

Cos(x)

arccos(x)

Can delete cos(x) in algebra

Just like exponents

Just like logs

Handy in algebra

Inverse function

Reverses whas cos(x) does

Backwards

Range

Switches with domain

Domain

Switches with range

Reverse machine

Is the X-Axis on the unit circle

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

Same amp

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

Because of radius

When the value exceeds 1 and neg 1

Figure out domain and modify

Divide by radius

Can be shown in graph

Same x coordinate when the phase shift is done

Same properties

Same Period

RRead "same Period"

Same zeros

when phase shift is modified by pi over 2

Same amplitude

Same period

Repeats itself every 2 times pi

Represented by y=cos(x)

One revolution around the unit circle

X goes to 1 the same as y goes to one

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

Same rate

Both make up the angle

One depends on other

Amplitude of one

Same as sin(x)

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

Graph has max and min of one

Period of Pi

Goes to -1 and back when x = pi