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 several ways. 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:
- 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:
- 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 center 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 center has an x value of less than 0, or is negative, while anything to the right has a positive value. Similarly, anything below the center 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:
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