Tangent
Tangent is opposite over hypotenuse. But using the using the caressing plane, it would be another branch to sine and cosine. Tangent is a very interesting operation. Tangent is found also in right triangles. But the tangent graph has asymptotes and its counterpart is cotangent, or 1/tan on a calculator or in a calculation. However, tangent is also a term used to mean touching at one point.
 To find the x intercepts of a tangent graph, use the equation N(π)

Math Joke of the week

Newlyweds A newlywed husband is discouraged by his wife's obsession with mathematics. Afraid of being second fiddle to her profession, he finally confronts her: "Do you love math more than me?" "Of course not, dear - I love you much more!" Happy, although sceptical, he challenges her: "Well, then prove it!" Pondering a bit, she responds: "Ok... Let epsilon be greater than zero..." 

Sine and Cosine

Sine, Cosine and Tangent are all based on a Right-Angled Triangle.

Before getting stuck into the functions, it helps to give a name to each side of a right triangle: triangle showing Opposite, Adjacent and Hypotenuse

"Opposite" is opposite to the angle θ"

Adjacent" is adjacent (next to) to the angle θ

"Hypotenuse" is the long one.

For a triangle with an angle θ, they are calculated this way:

Sine Function:sin(θ) = Opposite / Hypotenuse

Cosine Function:cos(θ) = Adjacent / Hypotenuse

It is important to memorize 45, 45, 90 triangles and their corresponding sides and well as the sides of 30, 60, 90 triangles.

Math Joke of the week 

Applying For A Job 

There are three people applying for the same job. One is a mathematician, one a statistician, and one an accountant. The interviewing committee first calls in the mathematician. They say "we have only one question. What is 500 plus 500?" The mathematician, without hesitation, says "1000." The committee sends him out and calls in the statistician. When the statistician comes in, they ask the same question. The statistician ponders the question for a moment, and then answers "1000... I'm 95% confident." He is then also thanked for his time and sent on his way. When the accountant enters the room, he is asked the same question: "what is 500 plus 500?" The accountant replies, "what would you like it to be?" They hire the accountant. 

Ch. 3 Summary :'(

So basically in the last month, we just been trying to solve functions. We factored, used complex numbers, and solved rational functions. Chapter 3 involves dividing polynomials in order to find zeros, the graph of a polynomial depends on its end behavior. Even degree polynomials with a positive coefficients go up but negative coefficients it goes down. Odd degree polynomials with a positive leading coefficient go down then up and if there is a negative coefficient it goes up then down. Using long division and synthetic division, you can find factors which consist of the zeros of the function. Also by plugging a number into a function, you can see if it is a zero by looking at the remainder. If the remainder is 0 then the number is a zero. By using the P/S equation you can find numbers that may or may not be zeros of a function. Check by using dividend and the remainder will determine if the number is a zero. The last part of the chapter involves finding asymptotes through methods such as factoring the denominator of a function, dividing leading coefficients.

Joke of the Week: 

I just finished reading Newton's Principia Mathematica, and found much of it to be rather derivative.

Rational Functions

All of these "rational" function have asymptotes. They are rational because they know not to reach certain places. 

A rational function is any function which can be defined by a rational fraction. For example, an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials do not need to be rational numbers, they may be taken in any field K.

The asymptotes are represented into dotted lines. The curved lines would be the functions. Note, the functions are not tangent to the asymptotes but are very close as it reach the end.

Joke of the week: 

The mathematician worked at home because he only functioned in his domain.