Learn Trigonometric Table With Tricks
What is Trigonometry?
Trigonometry is a branch of mathematics in which we study relationships between sides and angles of a triangle. Trigonometry works in all forms of geometry because every straight-sided figure can be divided into a set of triangles. In addition, trigonometry has surprisingly complex relationships with other branches of mathematics, especially complex numbers, infinite series, logarithms, and calculus.
What is Trigonometry Table?
A trigonometric table is a set of trigonometric ratio values for various standard angles, including other angles such as 0°, 30°, 45°, 60°, 90°, sometimes 180°, 270° and 360°. , in tabular format. Because of the patterns within trigonometric ratios and even between angles, it is easy to predict values from the trig table and use the table as a reference to calculate trigonometric values for various other angles. Trigonometric functions are sine function, cosine function, tan function, cot function, sec function, and cosec function.
What are Trigonometric values?
Trigonometry deals with the relationship between the sides of a triangle (a right-angled triangle) and its angles. Trigonometric value is a collective term for the values of various ratios such as sine, cosine, tangent, secant, tangent, and cosecant of a trigonometric table. All trigonometric ratios are related to the sides of a right-angled triangle and their values are found using the following ratios.
Steps to Create a Trigonometric Ratios Table
To make Trigonometric table students can follow the steps given below:
- Step 1: Make a table listing the top row of angles as 0°, 30°, 45°, 60°, 90° and write all trigonometric functions in the first column as sin, cos, tan, cosec, sec, cot.
- Step 2: To Find out the value of sin
Write down the angles 0°, 30°, 45°, 60°, 90° in ascending order and allocate them values 0, 1, 2, 3, 4 according to the order.
Like this 0→→0, 30→→1, 45→→2, 60→→3, 90→→4.
Divide the values by 4 and the square root of the entire value.
0° → √0/2 30° → 1 /2; 45° → 1/ √2; 60° → √3/2; 90° → √(4/4)
Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° | |
sin | 0° | 1/2 | 1/√2 | √3/2 | 1 |
- Step 3: Find the value of cos: sin (90° - x) = cos x. Use this formula to calculate cos x values. For example, cos 45° = sin (90° - 45°) = sin 45°. Similarly, cos 30° = sin (90° - 30°) = sin 60°. Using this you can easily find the value of cos function as,
Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° |
cos | 1 | √3/2 | 1/√2 | 1/2 | 0° |
- Step 4: To Find the value of tan: (tan x = sin x / cos x). Therefore, the value of the function tan can be constructed as,
Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° |
tan | 0 | 1/√3 | 1 | √3 | ∞ |
- Step 5: To Find the value of (cot x = 1/tan x). Therefore, the value of the cot function can be constructed as,
Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° |
cot | ∞ | √3 | 1 | 1/√3 | 0 |
- Step 6: To determine the value of cosec x: (cosec x = 1/sin x)
Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° |
cosec | ∞ | 2 | √2 | 2/√3 | 1 |
- Step 7: To determine the value of sec (sec x = 1/cos x)
Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° |
cosec | 1 | 2/√3 | √2 | 2 | ∞ |
For more detailed derivation you can check Trigonometric Ratios of Some Specific Angles
Tricks to remember trigonometry table
Memorizing trigonometry tables will help you in many ways and It’s not difficult to remember the table. If you know the trigonometric formulas, the trigger table is very easy to remember. The trigonometric ratio table is based on trigonometric formulas.
Below we are giving some simple trigonometric formulas. Start by memorizing these simple trigonometric formulas:
- sin x = cos (90° – x)
- cos x = sin (90° – x)
- tan x = cot (90° – x)
- cot x = tan (90° – x)
- sec x = cosec (90° – x)
- cosec x = sec (90° – x)
- 1/sin x = cosec x
- 1/cos x = sec x
- 1/tan x = cot x
Second Trick
Let&'s learn one hand trick to remember the trigonometric table easily! Set each finger at standard angles as shown in the picture. To fill in the sine values in the trigger table we'll include the number of fingers, while for the cosine table we'll just fill in the values in reverse order.
Image Source: wikimedia.org
- Step 1: For the sine table, count the fingers on the left side at a standard angle.
- Step 2: In this step, Divide the number of fingers by 4
- Step 3: Find the square root of the ratio.
Example
For the sin 60°, there are 3 fingers on the left. When 3 is divided by 4, we get (3/4). Finding the square root of the ratio (3/4) gives us the value of sin 60° = √3/2.
Like this, we can find out the values for sin 30°,45°,and 90°.
Trigonometry Ratios Table
Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° |
Angles(in Radians) | 0° | π/6 | π/4 | π/3 | π/2 |
sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |
cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
tan | 0 | 1/√3 | 1 | √3 | ∞ |
cot | ∞ | √3 | 1 | 1/√3 | 0 |
cosec | ∞ | 2 | √2 | 2/√3 | 1 |
sec | 1 | 2/√3 | √2 | 2 | ∞ |
Frequently Asked Question (FAQs)
Q1. What is the formula to find the value of the trigonometric function?
Ans. Trigonometry is a branch of mathematics in which we study relationships between sides and angles of a triangle. Trigonometry works in all forms of geometry because every straight-sided figure can be divided into a set of triangles.
Trigonometric Application:
- Trigonometry is used in cartography. Cartography is the creation of maps.
- Trigonometry is used in satellites and in the aviation industry.
- To describe sound waves we use trigonometric functions.
Q2. What is a Trigonometric function? how many types of trigonometric functions there is?
Ans . There are six basic trigonometric functions used in trigonometry. These functions are trigonometric ratios. The six basic trigonometric functions are sine, cosine, secant, cosecant, tangent, and tangent. Functions and trigonometric identities are the ratios of the sides of a right-angled triangle.The sides of a right-angle triangle are the vertices, hypotenuse, and base, which are used to calculate the values of sine, cosine, tangent, secant, cosine, and tangent using trigonometric formulas.
Some of the trigonometric formulas are given for more you can check Trigonometric Formulas
- Sin x = Opposite/Hypotenuse
- Cos x = Adjacent/Hypotenuse
- Tan x = Opposite/Adjacent
- Cot x = 1/Tan = Adjacent/Opposite
- Cosec x = 1/Sin = Hypotenuse/Opposite
- Sec x = 1/Cos = Hypotenuse/Adjacent
Q3. What are the application of Trigonometry in day-to-day life?
Ans. It may not have direct application in solving practical problems, but it is used in various fields. For example, trigonometry is used to develop computer music: you know, sound propagates in waves and this is through wave patterns, the sine or cosine function of computer music development. Trigonometry is used to measure the height of a roof, building, or mountain.
Q4. How to study trigonometry?
Ans. Trigonometry is a branch of mathematics. Trigonometry is the study of triangles. It is very easy if approached in the right way. Start with the right triangle, Clear your basics and take help from NCERT Solution for Maths Class 10