Quadrants

Quadrants:




Let X'OX and Y'OY perpendicular coplanar lines intersecting each other at O. We refer X'OX as x-axis and Y'OY as y-axis. It is clear from the adjoining figure, that these two lines divide the plane into four equal parts, each part is called a Quadrant.
The four Quadrants are:
XOY - first Quadrant
YOX' - second Quadrant
X'OY' - third Quadrant
Y'OX - fourth Quadrant

Trigonometry Heights and Distances

Trigonometry Heights and Distances:

• The word "Trigonometry" is derived from the two Greek words meaning measurements or solution of triangles. Trigonometry which is a branch of mathematics that deals with the ratio between the sides of a right triangle and its angles.
• Trigonometry is the study about relationships between the sides and angles of a triangle.
• Trigonometry is used in surveying and to determine Heights and Distances, in navigation it is to determine the location and the distances, and in the fields like nondestructive testing for determining things such as the angle for reflection or refraction of an ultrasound wave.

Types of Angles

Types of angles:

Algebra

Algebra is one of the main branches of mathematics. It explains the relations and properties of quantity by means of letters and other symbols. Algebra is used to simplify the long and very complicated statements. The basic algebra has the following subtopics are

1. Variables
2. Expressions
3. Terms
4. Polynomials
5. Equations.

Theorem in Mathematics

Theorem in Mathematics:

Congruent Supplements Theorem: When two angles are supplementary to the congruent angles or to the same angle, then the given angles are congruent.
Vertical Angle Theorem: Two angles are said as congruent even when they are vertical angles.
Alternate Interior Angle Theorem:Pairs of alternative interior angles are said as congruent when two parallel lines are cut transversely.
Consecutive Interior Angle Theorem:Pairs of consecutive interior angle are said as supplementary when two parallel lines are cut transversely.
Alternative Exterior Angle Theorem: Pairs of alternative exterior angle are said as congruent when two parallel lines are cut transversely.

Parabola equation

X intercept and Y intercept for Parabola equation:
The general form of parabola equation is
y = ax2 + bx + c where a,b and c are parts of the parabola.
Here, x intercepts are the roots of the equation of parabola. The x intercepts are the roots of the equation 0 = ax2 + bx + c. The very common methods to solve the equation are by factoring or by quadratic formula. The y intercept is (0 , c) for parabola equation.

Solve the equations Graphically

Solve the equations Graphically:

Check whether the pair of equations x + 3y = 6 and 2x – 3y = 12 is consistent. If so, solve them graphically.
Solution : Let us draw the graphs of the Equations (1) and (2). For this, we find two
solutions of each of the equations, which are given in Table

Plot the points A(0, 2), B(6, 0), P(0, – 4) and Q(3, – 2) on graph paper, and join the points to form the lines AB and PQ as shown in Fig below We observe that there is a point B (6, 0) common to both the lines AB and PQ. So, the solution of the pair of linear equations is x = 6 and y = 0, i.e., the given pair of equations is consistent.