Learning Basics of Trigonometry Formulas

Learning Basics of Trigonometry Formulas is a branch of mathematics that is less demand for red-tape and a fairly high level of difficulty that trigonometry. When compared with other branches of mathematics, trigonometry course rather difficult if the practice is connected with the real world and students prefer to memorize different types of trigonometric formulas.

For those who loved mathematics, a branch of mathematics which is not a big problem and makes complicated. However, instead it became a kind of game that's fun to be learned and conquered rather than feared. But, it must return to the character of the course each student is different. There is good in the use of the left brain and there is also a more developed right brain.

There are students who complain about the difficulty in trigonometry. Ie, when changing the value of special trigonometric angles in different quadrants. This is because there are so many formulas in trigonometry is a major factor in the difficulty of siswatersebut. They tend to memorize these formulas. Try to imagine, there are about 48 haris trigonometric formulas in mind, so much is not it ? After painstakingly memorized, yet they can be used in trigonometry problems are given.

Complicated, huh ? That's when learning mathematics by memorizing it. Not to understand the concept. The only way to learn math, especially trigonometry formula is easy to understand formula. Know ye that the trigonometric formulas that supposedly a lot of it was the result of a decrease of only some formula ? If you already understand the basic formulas and theories, no need to memorize dozens of formulas that seemed to head going to explode. Do not believe ? Just take a look at the decomposition of the following trigonometric formulas.

Parse the formula Trigonometry Basics

First let us describe the understanding of trigonometry. Is the calculation method in solving problems related to these comparisons in geometry, especially those to build a triangular shape. Trigonometry is also a branch of mathematics dealing with a large angle, which is very useful for counting the height of a particular form of the building or place without having to measure directly. Thus, more practical and efficient.

As a branch of mathematics that studies the proportion of the sides of a triangle, if viewed from one angle on a triangle, then it has some theoretical basis or certain basics. By understanding this basic theory, we can understand, use, also developed the theory into the following formulas.

• Angle sum formula
• Mid-point trigonometric formula
• Double angle trigonometric formula
• Sine and cosine multiplication formula
• Sum of sine and cosine formulas

1. Basic trigonometry formulas

Basic trigonometry formulas are as follows.

• sin alpha = y / r
• cos alpha = x / r
• tan alpha = y / x
• sec alpha = 1 / cos alpha = r / x
• cosec alpha = 1 / sin alpha = r / y
• Cotan alpha = 1 / tan alpha = x / y

And to memorize the trigonometric formulas consisting of sine, cosine, and tangent only by taking into account the right-angled triangle, it will display the following three terms :

• sin = to, ie sin = (front side angle) / (hypotenuse)
• cos = sami, the cos = (side angle) / (hypotenuse)
• tan = village, which is tan = (front side angle) / (side angle)

2. Special angle

As we will determine the value of a trigonometric function, there are many ways that can be used. Of them by using trigonometric tables, using a calculator, or use a special angle. The use of trigonometric tables are very useful when solving problems with arbitrary angles between 0.00 degrees to 90.00 degrees. So, with the trigonometric tables, can be searched for the value of trigonometric angle 37.6 degrees with fairly high accuracy results. The calculator can be useful when we examine the results have been obtained if it is correct or wrong.

3. Conversion angle

If the angle is outside the range of 0 degrees to 90 degrees then we can simplify the following rules :

• In the range of 90 degrees to 180 degrees to be: alpha = (180 - alpha)
• In the range of 180 degrees to 270 degrees to be: alpha = (alpha - 180)
• In the range of 270 degrees to 360 degrees to be: alpha = (360 - alpha)

4. Trigonometric ratio value based on the quadrant

If we simplify the corner, we should also look at the nature of the function of the quadrant position in which it resides.

• In quadrant I (0 degrees to 90 degrees): all comparisons trigonometry (sin, cos, tan, cosec, sec, Cotan) is positive.
• in quadrant II (90 degrees to 180 degrees): only the value of cosec sin and that is positive, others negative.
• in quadrant III (180 degrees to 270 degrees): only the value of tan and Cotan who are positive, others negative.
• in quadrant IV (270 degrees to 360 degrees): only the value of cos and secant are positive, others negative.

5. Trigonometric formulas add and subtract two points

Trigonometric formulas for the sum of two angles is as follows.

• sin (alpha + beta) = sin alpha + beta cos sin cos alpha beta
• cos (alpha + beta) = cos cos beta alpha - sin alpha sin beta
• tan (alpha + beta) = (tan tan alpha + beta) / (1 tan alpha x tan beta)

The trigonometric formulas for two-point reduction is as follows.

• sin (alpha - beta) = sin alpha beta cos - cos sin alpha beta
• cos (alpha - beta) alpha = cos cos + sin alpha sin beta beta
• tan (alpha - beta) = (tan alpha - tan beta) / (1 + tan tan alpha beta)

Actually, the formula for addition and subtraction of two angles is similar. It's just different on the plus and minus signs. Just take a look at the two forms of the formula. So, you just need to remember one form only, for example, the sum formula. By itself, the formula for reduction to be remembered as well.

6. Double angle trigonometric formula

To understand this trigonometric formulas, should remember the following trigonometric angle sum formula.

• sin (alpha + beta) = sin alpha + beta cos sin cos alpha beta
• cos (alpha + beta) = cos cos beta alpha - sin alpha sin beta
• tan (alpha + beta) = (tan tan alpha + beta) / (1 - tan x tan beta alpha)

This is because the shape of the formula is similar to the shape of a double angle trigonometric formulas. It's just the angle the same value, namely alpha = beta. So, we can replace the value of beta to alpha values.

Thus found to duplicate the following formula for the angle.

• sin (alpha + alpha) alpha = sin cos sin alpha alpha alpha + cos
• sin (2 alpha) = 2 sin cos alpha alpha
• cos (alpha + alpha) = cos alpha beta cos - sin sin alpha alpha
• cos (2 alpha) = cos ² alpha - alpha sin ²
• tan (alpha + alpha) = (tan alpha + tan alpha) / (1 - tan x tan alpha alpha)
• tan (2 alpha) = (2 tan alpha) / (1 - tan ² alpha)

7. Mid-point trigonometric formula

If we have got the formula for the trigonometric double angle formula derived from the development of the sum of angles, then we develop a double angle trigonometric formulas into the mid-point formula. The steps are as follows.

• sin alpha = plus or minus the root of (1 - cos alpha) / 2
• cos alpha = plus or minus the root of (1 + cos alpha) / 2
• tan alpha = plus or minus the root of (1 - cos alpha) / (1 + cos alpha)
• plus minus alpha = tan (sin alpha) / (1 + cos alpha)
• plus minus tan alpha = (1 - cos alpha) / (sin alpha)

8. Multiplication formula trigonometry sine and cosine

Trigonometric formulas sine and cosine multiplication is a development of the angle sum formula using the method of elimination and substitution. The result will be obtained following multiplication formula.

• alpha sin beta = cos {sin (alpha + beta) + sin (a - ß)}
• cos a sin ß = ½ {sin (a + ß) - sin (a - ß)}
• cos a cos ß = ½ {cos (a + ß) + cos (a - ß)}
• sin a sin ß = - ½ {cos (a + ß) - cos (a - ß)}

9. Addition and subtraction formula of sines and cosines

Basic trigonometric formula is different from the angle sum formula. This is because the sum is not angular, but trigonometrinya function. This formula can be developed from the multiplication formula of sines and cosines. The result is the following formulas.

• sin a + sin ß = 2 sin ½ (a + ß) ½ cos (a - ß)
• sin a - sin ß = 2 cos ½ (a + ß) ½ sin (a - ß)
• cos a + ß = 2 cos cos ½ (a + ß) ½ cos (a - ß)
• cos a - cos ß = - 2 sin ½ (a + ß) ½ sin (a - ß)

Wise Ways of Learning Formulas Trigonometry

It would be nice if all that was not memorize the trigonometric formulas. This is because so many and likely to be able to memorize all these formulas will make your head hot enough. But to understand the intricacies of the theory of trigonometry, we can finally understand all the trigonometric formula as a whole. To help understand trigonometry, you can use the help of the drawings.

For students who are studying the basics of trigonometry, it is better not to forgeted methods given by the teacher and still learning every trigonometric formulas found in textbooks. And do not forget to continue to practice with answering questions in trigonometry textbook.

Because the real branch of mathematics that one is very useful when we apply it in real life. And very useful for other scientific branches, such as architecture, urban design, landscape science, and others. So that all forms of knowledge of mathematics is very useful to be applied to other scientific branches. Such as trigonometric formulas that are specifically studying the value and slope angle. If there are errors in the writing of this article, we apologize and instructions. thank you