- April 5, 2021
- Posted by: Fliplearn
- Category: Generic
Derived from clubbing the words – “Trigonon” and “Metron”, trigonometry means triangle and measure respectively. Trigonometry is one of the significant divisions of Mathematics that helps find angles and missing sides. The trigonometry associates with the right – angled triangle, wherein one of the three angles is a right angle. This helps simply a variety of geometrical problems. Trigonometry helps in simplifying calculations and solves a wide variety of geometrical problems. It is used for the wide applications like – construction of houses and cars. Infact, the technology used in computer graphics, navigation medical imaging etc. is developed using trigonometry.
What is Trigonometry Table?
A trigonometry table consists of ratios like sine, cosine, tangent, cosecant, secant, and cotangent. In short, these ratios are written as sin, cos, tan, cosec, sec, and cot. The trigonometric ratios help find the values of trigonometric standard angles that include – 0 degree, 30 degree, 45 degree, 60 degree and 90 degree. It also helps find standard angles like 180 degree, 270 degree and 360 degree in the tabular format.
While Studying Trigonometry, Keep the Following Things in Mind:
- Sides and angles that touch are known as adjacent. Hence, every side has two adjacent angles.
- Sides and angles that do not touch each other are known as opposite.
- In a right angle triangle, the side opposite the right angle is known as hypotenuse, but the two remaining sides are known as legs.
- If two angles or two sides are given, they can be worked used to measure the rest of the details.
Tricks to Remember Trigonometry Table Formula
1. Firstly, Learn the Basics
Firstly, it is important to learn the basics. Trigonometry works for right angled triangle. The right angled triangle consists of three areas – Perpendicular (P), Hypotenuse (H) and Base (B). Basics not only helps you remember the ratios, but also helps a lot in solving trigonometry problems, especially related to height and distance problem.
Image Courtesy: www.quora.com
Sin (Theta) = P/H, Cos (Theta), B/H, Tan (Theta) = P/B
P – Perpendicular, B – Base and H – Hypotenuse
The right angled triangle ABC is right angled at B, with angle ‘Ɵ’ at C.
2. Remember the Hindi Mnemonic
Sin (Theta) = Perpendicular/Hypotenuse, Cos (Theta) = Base/Hypotenuse and Tan (Theta) = Perpendicular / Base. Now, the point is how you would remember this? That’s when the role of Hindi mnemonic plays an important role. Pandit Badri Prasad, Har Har Bole.
Sin (Theta) Cos (Theta) Tan (Theta)
Pandit (P)/ Badri (B)/ Prasad (P)/
Har (H) Har (H) Bole (B)
3. Reverse of Sin, Cos, and Theta is Sec, Cosec and Cot respectively
Once you remember the ratio of sin, cos and tan, then you can easily remember sec, cosec and tan. Sec, cosec and tan are the reverse of sin, cos and theta respectively.
Sec = 1/cos which is reciprocal of cos
Cosec = 1/sin which is reciprocal of sin
Cot = 1/tan which is reciprocal of tan
Steps to Create a Trigonometric Table
1. Create a Blank Trigonometry Table
Draw a Trigonometry table formula having 6 rows and 6 columns. In the columns, write down all the trigonometric rations (sine, cosine, tangent, cosecant, secant and cotangent). In the rows, write down the commonly used angles in trigonometry (0 degree, 30 degree, 45 degree, 60 degree and 90 degree.) You can leave the other entries blank.
2. Fill the Values for the Sine Row
Use the expression √x/2 in order to fill the blank entries in this row. The value x should be that of the angle listed on the left-hand side of the table. This formula helps to calculate the sine values for 0°, 30°, 45°, 60°, and 90° and write those values in your trigonometry table.
3. Fill in the Sine Row Entries in the Cosine Row in a Reverse Order
In order to fill in the cosine row of trigonometry table, reverse the sine row entries. The cosine column should be entered in a way that the value for the sine of 90 degree is used as the value for the cosine of zero degree. The value of the sin 60 degree becomes the value for the cosine 30 degree and so on.
4. Fill the Tangent Row by Dividing the Sine Values by the Cosine Value
Take the sine value and divide it by its cosine tangent = sine/cosine. Thus, for every angle, take its sine value and divide it by its cosine value in order to calculate the corresponding tangent value.
5. Reverse the Entries of Sine Row and Fill Them in a Parallel Manner in the Cosecant Row
As the cosecant of an angle is equal to the inverse of the sine of that angle. Hence, we need to simply reverse the entries of sine row and fill them in the cosecant row in the parallel manner.
6. Reverse the Entries of Cosine Row and Fill Them Parallel in Secant Row
Starting from the cosine of 90°, reverse the values of cosine row and then fill them in the secant row. For ex – Value of cosine for 0 degree i.e. 1 needs to be reversed that is 1/1 which again becomes the value of secant for 0 degree. Similarly the value of cosine for 30 degree i.e. under root 3 by 2 will become 2 by under root 3 as the value of secant for 30 degree.
7. Fill the Cotangent Column by Reversing the Values of the Tangent Row
The value for the tangent of 90 degree will become the value for 0 degree in the cotangent row. Same will be done for the 60 degree of tangent, which will become the 30 degree of cotangent and so on.
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Frequently Asked Questions About Trigonometry Table
Q1. What is Trigonometry?
Ans. Trigonometry is the branch of Mathematics that deals with the relationship between angles and side lengths of triangles.
Q2. What is Trigonometry Table?
Ans. Trigonometry table is simply a collection of trigonometric values of a lot of standard angles which include 0°, 30°, 45°, 60°, 90°, sometimes with other angles also like 180°, 270°, and 360° included, in a tabular format.
Q3. Who Invented Trigonometry?
Ans. Trigonometry began with the Greeks. Hipparchus was the first person who constructed a table of values for a trigonometric function.
Q4. Mention the Applications of Trigonometry?
Ans. Trigonometry is applicable in various fields like seismology, oceanography, physical sciences, astronomy, meteorology, acoustics, navigation, and electronics. It is also helpful in measuring the height of the mountain, finding the distance between long rivers etc.