Wednesday, April 27, 2011

Try to find a and b

Given that i^2 = -1 find values for a and b.

Solution can be found here.

Thursday, April 21, 2011

A Picture That Makes Me Happy


Well this picture doesn't really make me happy but I like it because of the maths joke. Anyways most people would know that pi is an irrational number. As for i, it is known as the imaginary unit where 1^2 = -1. You should know that -1 cannot be square rooted with with advanced mathematics it can be.

Thanks to Raymond G for linking me to this image.

Monday, April 11, 2011

Trigonometry

Trigonometry is the study of triangles and the relations between their sides and angles. There are three main trigonometric functions namely: Sine, Cosine and Tangent (Sin, Cos, Tan).
In a right angled triangle, Sin = Opposite/Hypotenuse Cos= Adjacent/Hypotenuse Tan= Opposite/Adjacent
The easy way to remember this is by remembering SOHCAHTOA.

These ratios can be extended in order for it to work out unknown side or angles of non-right angled triangles.



The area of a triangle can also be determined by using trigonometry.
Proofs for the Sin and Cos rules and the Area of triangle formula can be found here.

Unit Circle
The unit circle can be used to find the the Sin, Cos and Tan of angles greater than 90 degrees. A unit circle is a circle where the radius is equal to 1 unit.

Exact Values
The easy way to remember these exact values is that Sin 0, 30, 45, 60 and 90 are √0/2, √1/2, √2/2, √3/2 and √4/2 (1) respectively. The same goes for Cos except the order is reversed. To work out Tan, you simply have to divide Sin by Cos. Click on the images to view an enlarged version.