Follow the table of sines and cosines here. Check the calculators and tables for trigonometric functions like sines and cosines. Refer to trigonometry ratio tables and also tricks to remember the trigonometry table. Know the various steps involved in preparing the trigonometry table and the determination of values to it. Check the below sections to know the various details regarding sine and cosine tables and calculations.
Table of Sines and Cosines
Trigonometry is the most important concept in mathematics which involves the lengths and areas of a triangle. These are mostly associated with right-angle triangles where one of those angles is 90 degrees. Trigonometry has a huge number of applications in various fields of Mathematics. Geometric Calculations can easily be figured out using trigonometric values, formulas, and functions as well. In the below sections, we are providing the trigonometric ratios table which helps to find the trigonometric standard angle values like 0°, 30°, 45°, 60°, and 90°, etc.
Various trigonometric ratios like sine, cosine, tan, secant, cotangent are present. In short, these ratios can be defined as cosec, sec, sin, cos, tan, cot. With the help of these ratios, trigonometric problems can easily be solved and you can calculate various mathematical derivations. Hence, it is necessary for you to learn and remember the trigonometric values of the standard angles.
The trigonometric ratio tables are mostly used to calculate the number of areas. In today’s world, trigonometry is used for science, navigation, and engineering. The ratio tables were effectively used in the era of pre-digital, where the pocket calculators were not available. The most essential application of trigonometric ratio tables is FFT(Fast Fourier Transform) algorithms.
Trigonometric Ratios Table
| Angles (In Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
|---|---|---|---|---|---|---|---|---|
| Angles (In Radians) | 0° | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |
| tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |
| cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |
| cosec | ∞ | 2 | √2 | √2/3 | 1 | ∞ | -1 | ∞ |
| sec | 1 | √2/3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
Tips and Tricks to Remember Trigonometric Table
Remembering the trigonometric table is a tough task for the students. But, if you follow a few tips and tricks, you can easily remember it. If you remember the table, you can easily solve many questions. The first step you have to do to remember the table is to get perfection in trigonometric formulae. The ratio table completely depends on the trigonometric formulae. We are providing a few steps to remember the trigonometric table.
Before, knowing the tricks to remember a table, look at the important formulae which helps you to prepare a table.
- cot x = tan (90° – x)
- cosec x = sec (90° – x)
- sin x = cos (90° – x)
- 1/cos x = sec x
- tan x = cot (90° – x)
- cos x = sin (90° – x)
- sec x = cosec (90° – x)
- 1/sin x = cosec x
- 1/tan x = cot x
Also, read:
- Worksheet on Trigonometric Identities
- Trigonometrical Ratios Table
- Trigonometrical Ratios of 90 Degree Minus Theta
How to Create a Trigonometry Table
Step 1:
Starting creating a table with angles on the top row listing. The angles must be 0°, 30°, 45°, 60°, 90°, 180°, 270°, 360°. Once you include all the angles as columns, now include all the trigonometric functions as rows. Include functions like sin, cos, tan, cosec, sec, cot, etc.
Step 2:
In this step, we have to determine the values of sin, we have to divide the values of 0,1,2,3,4 by 4, and next we have to take the square root. For suppose, if you have to find the value of 0°, we have to write √(0/4) which results as 0. Now, find the value of 30°, we have to write √(1/4) which results as 1/2. Now, find the value of 45°, we have to write √(2/4) which results in 1/√2. In the same way, we have to find the values of the remaining angles. Hence the final table values of sin will be as follows.
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |
Step 3:
In the next step, we have to determine the values of cos for all the required angles. The cos values are the opposite of the sin values which means that the value of sin(0-x) is similar to the value of cos(90-x). To find the value of cosine divide the values with 4 in the opposite order of sin i.e., 4, 3, 2, 1, 0 by 4 and take the square root.
For suppose, to find the value of 0°, we have to write √(4/4) results as 1. To find the value of 30°, we have to write it as (√3/4) results as √3/2. To find the value of 45°, we have to write as (√2/4) results as 1/√2. In the same way, we have to find the values of the remaining angles. Hence the final table values of cos will be as follows.
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |
Step 4:
Now, determine the values of a tangent for all the required angles. The formula to find the tangent values is tan x = sin x/cos x. To find the value of tan, use the formulae mentioned above. To find the value of tan 0°, use the values of sin and cos, i.e., we have to use the formula tan 0° = sin 0°/cos 0° which is 0/1 and results in 0. To find the value of 30°, tan 30° = sin 30°/cos 30° which is (1/2) / (√3/2), results in 1/√3. In the same way, find the values of the remaining angles. Hence the final values will of tan will be as follows.
| tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |
Step 5:
In Step 5, we have to determine the value of the cot. The cot values are the opposite of the tan values which means that the value of tan(0-x) is similar to the value of cot(90-x). To find the value of cot, we have to take the value as 1/tan. To find the value of 0°, use the value of 1/tan 0° which is 1/0 = ∞. To find the value of tan 30°, use the value as 1/tan 30° which is 1/(1/√3) = √3. In the same way, find the values of the remaining angles. Hence the final values will of the cot will be as follows.
| cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |
Step 6:
In the next step, we have to determine the value of cosecant. The cos values are the inverse of the sin values. To find the value of cos, we have to take the value as 1/sin. To find the value of 0°, use the value of 1/sin 0° which is 1/0 = ∞. To find the value of cos 30°, use the value as 1/sin 30° which is 1/(1/2) = 2. In the same way, find the values of the remaining angles. Hence the final values will of cos will be as follows.
| cosec | ∞ | 2 | √2 | √2/3 | 1 | ∞ | -1 | ∞ |
Step 7:
In the last step, we determine the value of the secant. The sec values are the inverse of the cos values. To find the value of sec, we have to take the value as 1/cos. To find the value of 0°, use the value of cos 0°, 1/cos 0° which is 1/1 = 1. To find the value of cos 30°, use the value as 1/cos 30° which is 1/1/√3 = √2. In the same way, find the values of the remaining angles. Hence the final values will of sec will be as follows.
| sec | 1 | √2/3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
FAQs on Table of Sines and Cosines
1. What is Trigonometry?
Trigonometry is the mathematics branch which deals with angles and sides of the triangle.
2. What are the Trigonometric Functions and their Types?
Trigonometric functions are defined for the functions of the right-angled triangle. There are 6 basic trigonometric function types. They are:
- Sin function
- Cos function
- Tan function
- Cot function
- Sec function
- Cosec function
3. Find out the Values of the Trigonometric Functions?
There are various values of all the trigonometric functions
- Cosec = 1/Sin = Hypotenuse/Opposite
- Sec = 1/Cos = Hypotenuse/Adjacent
- Sin = Opposite/Hypotenuse
- Cos = Adjacent/Hypotenuse
- Tan = Opposite/Adjacent
- Cot = 1/Tan = Adjacent/Opposite