All these functions are based on something called the "unit circle". These functions tell you all sorts of neat stuff about angles. First you must understand the properties of vectors. Any vector can be broken down into its x & y components. With this you can find the angle measure of the angle . Why is this important you ask? By definition a vector quantity must have a magnitude and direction. We know that tan = . Using the properties of inverses = tan^-1. Using the x-axis as one of the rays of the angle. If I told you that x = 6 & y = 8 the n you would find the value of using a trigonometric table or a scientific calculator to be 53.1°. The final vector would be represented as 10 units [E 53.1° S]. Further discussion on vectors can be found in chapter one section 3.

Sin & cos are functions. Just like f(x) is a function on x, sin or cos are functions on . In function notation we define f(x) as such: f(x) = 3x + 2. So whenever we see f(x) we must think 3x + 2. Lets say we had f(4). what would the solution to the function be? f(4) = 14 or f(4) = 3(4) +2 = 14. The sine and cosine functions must be looked at the same way. Although an explanation of the mathematics behind these functions is beyond the scope of this book, knowing the properties of these functions is important.

You should memorize the cos, sin, & tan of the first five degree measures (0° - 90°). From those you can figure out all the others. The following are some very useful trigonometric identities. They are used when solving algebraic equations & expressions that involve trigonometric functions.

As we said earlier trigonometric functions are very important to triangles. The law of sines and the law of cosines are two laws which allow you to solve for unknown angles or sides of a triangle.

In order for the law of cosines to be useful you must be given or have some way to derive two of the sides of the triangle and the included angle between them or all three sides.

To use the law of sines you need to know two angles and the included side or two sides and an angle besides the included angle.