Complete Package of Basic Principles and Study Materials for Learning Algebra and Trigonometry In a Row

Mathematics is a very interesting subject. Algebra and Trigonometry are one of the most important areas of Mathematics. It is connected to our daily life in a several way. Everyone should have a sound knowledge of Algebra and Trigonometry. Here we made a complete package of basic principles of algebra and trigonometry and study materials all in one place.


Basic Algebra Principles:

  1.  a (b + c) = ab + ac

This is known as the Distributive Property of Multiplication. If you're multiplying something with a sum of two or more other terms, you can distribute your multiplication to each of the terms.

Example: 2 (3 + 5) = 2 * 3 + 2 * 5

 a (b / c) = ab / c

Any multiplication or division of the numerator of a fraction applies to the fraction as a whole, and vice versa: if you need to multiply a fraction, multiply the numerator and your aim is achieved.

Example: 2 * (3 / 4) = (2 * 3) / 4

 (a / c) / b = a / bc

If you divide the numerator by a particular number, it has the same effect on the fraction's overall value as if you multiply the denominator by that same number.

Example: (1 / 5) / 2 = 1 / 10

 a / (b / c) = ac / b

Like the previous one, dividing the denominator of a fraction has the same effect as multiplying the numerator.

Example: 1 / (3 / 2) = (1 * 2) / 3 = 2 / 3

(a / b) + (c / d) = (ad + bc) / bd

It shows the fact that, we can find a common denominator between two fractions by multiplying the numerator and denominator of each fraction by the other's denominator.

Example: 3 / 5 + 1 / 3 = (1 * 5) + (3 * 3) / (3 * 5)

(a / b) - (c / d) = (ad - bc) / bd

This is just the another form of rule 5, but for subtraction of two fractions, rather than addition.

Example: 3 / 5 - 1 / 3 = (3 * 3) - (1 * 5) / (3 * 5)

(a - b) / (c - d) = (b - a) / (d - c)

Example: 3 - 5 / 2 - 1 = -2

 8. (a + b) / c = a / c + b / c

This is simply a result of the fact that two fractions with common denominators can be added by adding the numerators and leaving the denominator unchanged.

Example: (2 + 2) / 4 = 2 / 4 + 2 / 4 =1

9. ac + bc / c = a + b

Example: (4 * 5) + (2 * 5) / 5 = (4 * 5) / 5 + (2*5) / 5

10. (a / c) / (b / d) = ad / bc

This is a combination of rule 3 and 4.

Example: (4 / 5) / (2 / 1) = (4 * 1) / (2 * 5)


Basic Trigonometry Principles:

  1. Right-Angled Triangles

  • The right-angle is indicated by the little box in the corner.
  • The other angle is indicated by the 'Theta'.
  • The opposite side of the right angle, which is the largest, is known as Hypotenuse (H).
  • The opposite side of 'Theta', is called as Opposite (O).
  • The side next to 'Theta', is called as Adjacent (A).


 2. There are three basic functions in trigonometry, each of which is one side of a right-angled triangle divided by another. These three functions are:


Calculating Sine, Cosine and Tangent:



3. Graphs of Sine, Cosine and Tangent





4. Trigonometry in a Circle

Consider, a circle divided into four quadrants. Conventionally, the centre of the circle is considered as the Cartesian Coordinate of (0,0). That is, the x value is 0 and the y value is 0. Anything to the left of the centre has an x value of less than 0, or is negative, while anything to the right has a positive value. Similarly anything below the centre point has a y value of less than 0, or is negative and any point in the top of the circle has a positive y value.



Best Study Materials for Learning Algebra and Trigonometry:

 

This is one of the most popular online study material in the world. It has tons of tutorials of every topic. Anyone can learn anything very easily from here. It is completely free and useful. Anybody can learn anything whenever they get time.The courses are very helpful and especially when helping out on homework. The instructors are very qualified and friendly. The courses are easy to understand and follow. The objectives are well explained with multiple different ways. Once you start to learn, you'll definitely gonna love it.

It is the all in one for the Math lovers. You can get everything related to the math. Free videos with nice presentation can make you more motivated. Please have a look and learn algebra and trigonometry very efficiently and effectively.

This is one of the best school for learning throughout the world. It is initiated to provide a new model for the dissemination of knowledge. It's a dream to study here. Here you will get free lectures, notes, exams and guideline to learn algebra and trigonometry. Everything is completely free and you can get from anywhere.

Books are the best supplement for learning anything well concisely. It will provide everything you need and make yourself a pro. Books are the best comprehensive reference and it will provide you the complete outline in brief. There are several books written by the experts which will help you to go through step-by-step. Make a start and shape up your plan to learn in a more efficient and effective way. For learning algebra and trigonometry, you can take a look on: Best Algebra and Trigonometry Books.
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