Introduction to Angleshttp://www.blogger.com/img/blank.gif

Let us study about Angles :

An angle is a measure of rotation. Angles are measured in degrees. One complete rotation is measured as 360°. Angle measure can be positive or negative, depending on the direction of rotation. The angle measure is the amount of rotation between the two rays forming the angle. Rotation is measured from the initial side to the terminal side of the angle. Positive angles (Figure 1 a) result from counterclockwise rotation, and negative angles (Figure 1 b) result from clockwise rotation. An angle with its initial side on the x-axis is said to be in standard position.

Figure 1 (a) A positive angle and (b) a negative angle. Angles that are in standard position are said to be quadrantal if their terminal side coincides with a coordinate axis. Angles in standard position that are not quadrantal fall in one of the four quadrants, as shown in Figure 2 . Hope the above explanation helped you.

Points, Lines, and Planes

Let us learn about Points, Lines and Planes,
Point, line, and plane, together with set, are the undefined terms that provide the starting place for geometry. When we define words, we ordinarily use simpler words, and these simpler words are in turn defined using yet simpler words. This process must eventually terminate; at some stage, the definition must use a word whose meaning is accepted as intuitively clear. Because that meaning is accepted without definition, we refer to these words as undefined terms. These terms will be used in defining other terms. Although these terms are not formally defined, a brief intuitive discussion is needed.
Point
A point is the most fundamental object in geometry. It is represented by a dot and named by a capital letter. A point represents position only; it has zero size (that is, zero length, zero width, and zero height). Figure 1 illustrates point C, point M, and point Q.

Figure 1 Three points.

Line

A line (straight line) can be thought of as a connected set of infinitely many points. It extends infinitely far in two opposite directions. A line has infinite length, zero width, and zero height. Any two points on the line name it. The symbol ↔ written on top of two letters is used to denote that line. A line may also be named by one small letter (Figure 2 ).

Figure 2 Two lines.

Collinear points

Points that lie on the same line are called collinear points. If there is no line on which all of the points lie, then they are noncollinear points. In Figure 3 , points M, A, and N are collinear, and points T, I, and C are noncollinear.

Figure 3 Three collinear points and three noncollinear points.

Plane

A plane may be considered as an infinite set of points forming a connected flat surface extending infinitely far in all directions. A plane has infinite length, infinite width, and zero height (or thickness). It is usually represented in drawings by a four-sided figure. A single capital letter is used to denote a plane. The word plane is written with the letter so as not to be confused with a point (Figure 4 ).

Figure 4 Two planes.

Hope the above explanation helped you.

Relations between Angles and Sides in Triangles

Let us understand what is the relations between Angles and Sides in Triangles,

he following list summarizes the most important relationships between the angles and the sides in an arbitrary triangle:
* The sum of the angles in a plane triangle is always constant and equal to 180° (= p radiants).
a + b + g = 180°.

Please note that the sum of the angles deviates from 180° if the triangle is not on a plane. For example, drawing a triangle on the surface of a sphere may result in a sum of the angles of 270°.

* If two sides (a and b) of a triangle are of equal length then the angles n and n are equal.

* The sum of the outer angles is always 360° (2p)
a + b + g = 360°.

* The sum of the lengths of two sides is always greater than the third side, any side is greater than the absolute value of the difference of the other two sides:
a + b > c > |a-b|
a + c > b > |a-c|
c + b > a > |c-b|

Hope the above explanation helped you..

Sine and Cosine

Let us learn about Sine and Cosine :

This relationship is expressed by the two most fundamental equations of trigonometry:

x = r × cos θ
y = r × sin θ

Or, equivalently:

cos θ = x/r
sin θ = y/r

Sin (sine) is the ratio of the vertical side (the side opposite the corner we're looking at) to the hypotenuse. Cos (cosine) is likewise the ratio of the horizontal side (the side adjacent to that corner) to the hypotenuse. Sine and cosine are functions, which is to say that they take one number (an angle in this case, usually expressed in degrees or radians) and spit out another. For certain values of θ, it is easy to figure out what the sine and cosine values are going to be just by thinking about what the angle corresponds to on the circle; the simplest cases are for θ = 0°, which is a line pointing right, giving cos θ = 1 and sine θ = 0; a line pointing straight up (ie. θ = 90°), which gives us cos θ = 0 and sine θ = 1, and so on. At 45° the opposite and adjacent sides are the same length, so from Pythagoras' Theorem (r2=x2 + y2) they must each be (√2)/2. For values in between the sine and cosine vary in a smooth curve, so that a plot of sin x against x is your basic wavy line:

Cosine is to sine as horizontal is to vertical, so the graph of cosine is just like the graph of sine shifted by one quarter-turn. On a graph together, they look like this:

Hope the above explanation helped you..

Theoretical probability

First of all let us understand what is theoretical probability,

The theoretical probability (also called classical probability) of an event E,
written as P(E), is defined as
where we assume that the outcomes of the experiment are equally likely.

We will briefly refer to theoretical probability as probability.

This definition of probability was given by Pierre Simon Laplace in 1795.

Probability theory had its origin in the 16th century when
an Italian physician and mathematician J.Cardan wrote the
first book on the subject, The Book on Games of Chance.
Since its inception, the study of probability has attracted
the attention of great mathematicians. James Bernoulli
(1654 – 1705), A. de Moivre (1667 – 1754), and
Pierre Simon Laplace are among those who made significant
contributions to this field. Laplace’s Theorie Analytique
des Probabilités, 1812, is considered to be the greatest
contribution by a single person to the theory of probability.
In recent years, probability has been used extensively in
many areas such as biology, economics, genetics, physics,
sociology etc.
Hope the above explanation helped you, now let me give you examples on probability.