Chocolate math

Love math - Put on your positive thinking hat

I love math. Who doesn't?
If you don't it must be because you haven't met with its amazing properties and applications.

For many people it's understanding math that is the problem and from that the negativity spirals out onto those around them and hence the general dislike of mathematics.

I believe that everyone are able to do math and understand the basic ideas, excluding perhaps all the complicated concepts one might encounter past a first year university level. The problem is the attitude going in, the believe that you cannot do something before you even tried. With that kind of thinking no one will ever get anything done.

Let's all put on own positive thinking hats wherever we go in this world and not only embrace math, but all seemingly difficult tasks that are throw unto our paths everyday. The next time someone wants to teach you something about math, say yes and you might just be surprised.

Our minds can store an endless amount of information so why not use some of that space to learn something new and interesting every day?

Happy positive thinking!

How not to expand an equation

The correct answer would be:


and we can make use of the Binomial theorem to find all the other terms.

Trigonometry Series (Part 4)

Today we look at several formulas which tend to be helpful when we are solving trigonometric equations or working with specific angles. They are also useful for simplifying expressions.

Addition formulas:


The formula for tan can be derived by making use of the formulas for sin and cos.


Subtraction formulas:

 
The subtraction formulas can be easily derived from the addition formulas by making use of the angle identities in Part 3.

Double-angle formulas:


These formulas can be derived from the addition formulas by letting y=x and using some identities.

Half-angle formulas:



These formulas can be obtained by rewriting the double-angle formulas.

Next time we will consider a few problems and examples, showing how we can apply and use all the information that we have from the previous parts in the series.

Trigonometry Series (Part 3)

The following identities come in very useful when we are solving equations of trigonometric functions.

This is the basic identity

and these two can be derived from the first identity


taking note that



These following angle-identities can easily be derived if we take a look at the graphs of he respectively functions (see Trigonometry Series (Part 1)).






Consider any triangle, it need not be right-angled,



then there are two laws that can help us to calculate angles or side length of a triangle, given that we have the information about three other angles and/or sides of the triangle.
 
Law of Sines

 

Law of Cosines:



Next time we take a look at some useful formulas.