Trigonometry Table: Ratios, Tricks, and Solved Examples

Written ByPriya WadhwaLast Modified 07-06-2022

Trigonometry Table: Trigonometry is a popular branch of Mathematics that deals with the study of triangles and the relationship between the length of sides and angles in a triangle. It has a wide range of applications in astronomy, architecture, aerospace, defence, etc. In this article, we have provided the kanalbdg.com trigonometry tables containing the values of all trigonometric ratios for the most commonly used angles. 

The trigonometry table is a useful tool for finding the values of trigonometric ratios for standard angles such as 0°, 30°, 45°, 60°, and 90°. It comprises the values of trigonometric ratios – sine, cosine, tangent, cosecant, secant, cotangent, also known as sin, cos, tan, cosec, sec, and cot, respectively. Using the trigonometry table formula, students can compute trigonometric values for various other angles by understanding the patterns seen within trigonometric ratios and between angles.Latest Update

👉 The CBSE Class 10 Term 1 Results were announced on March 11, 2022, and Class 12 Term 1 Results were announced on March 15, 2022. Students can enter their roll numbers and check the results on their official website – cbseresults.nic.in.👉 The CBSE Term 2 Examinations for Classes 10 and 12 kanalbdg.com will commence on April 26, 2022. 👉 Regular students can check the CBSE Exam Date Sheet 2022 from the official website of CBSE – cbse.nic.in and cbse.gov.in.Introduction to Trigonometric Table

In simple words, the trigonometric table is a collection of the values of trigonometric ratios for the commonly used standard angles including 0°, 30°, 45°, 60°, and 90°. Sometimes it is also used to find the values for other angles like 180°, 270°, and 360° in the form of a table. Various patterns exist within trigonometric ratios and between their corresponding angles. Therefore, it is easy to predict the values of the trigonometric table and also use the table as a reference to calculate trigonometric values for other non-standard angles. The various trigonometric functions in Mathematics are sine function, cosine function, tan function, cot function, sec function, and cosec function.

Before beginning, let us try to recall the trigonometric formulas listed below.\(\sin x=\cos \left(90^{\circ}-x\right)\)\(\cos x=\sin \left(90^{\circ}-x\right)\)\(\tan x=\cot \left(90^{\circ}-x\right)\)\( \cot x= \tan \left(90^{\circ}-x\right)\)\(\sec x=\operatorname{cosec}\left(90^{\circ}-x\right)\)\(\operatorname{cosec} x=\sec \left(90^{\circ}-x\right)\)\(\frac{1}{ \sin x}=\operatorname{cosec} x\)\(\frac{1}{ \cos x}=\sec x\)\(\frac{1}{\tan x}=\cot x\)Trigonometric Values

Trigonometry is the study of the relationship between the sides of a triangle (right-angled triangle) and its angles. The term trigonometric value is used to collectively define values of different ratios, such as sine, cosine, tangent, secant, cotangent, and cosecant in a trigonometric table. Every trigonometric ratio is connected to the sides of a right-angled triangle, and the trigonometric values are found using these ratios.Standard Angle Trigonometry Tables

The trigonometry ratio table is essentially a tabular collection of values for trigonometric functions of different conventional angles such as 0°, 30°, 45°, 60°, and 90°, as well as unusual angles such as 180°, 270°, and 360°. Because of the patterns that exist within trigonometric ratios and even between angles, it is simple to anticipate the values of the trigonometric ratios in a trigonometric table and use the table as a reference to compute trigonometric values for different other angles.

Trigonometric ratios – sine, cosine, tangent, cosecant, secant, and cotangent – are listed in the table. Sin, cos, tan, cosec, sec, and cot are the abbreviations for these ratios. The values of the trigonometric ratios of these standard angles are best remembered.

Learn Exam Concepts on EmbibeSteps to Create a Trigonometric Table

Students can follow the steps given below to make a sin cos tan table.

Step 1: Create a table with the angles \(0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}\), and \(90^{\circ}\) on the top row and all trigonometric functions \(\sin , \cos , \tan , \operatorname{cosec}, \mathrm{sec}\), and cot in the first column.

Step 2: Determine the value of \(\sin\).Write the angles \(0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}\) in ascending order and assign them values \(0,1,2,3,4\) according to the order. So, \(0^{\circ} \rightarrow 0 ; 30^{\circ} \rightarrow 1 ; 45^{\circ} \rightarrow 2 ; 60^{\circ} \rightarrow 3 ; 90^{\circ} \rightarrow 4\).

Then divide the values by \(4\) and square root the entire value. \(0^{\circ} \rightarrow \sqrt{\frac{0}{4}}=0 ; 30^{\circ} \rightarrow \sqrt{\frac{1}{4}}=\frac{1}{2} ; 45^{\circ} \rightarrow \sqrt{\frac{2}{4}}=\frac{1}{\sqrt{2}} ; 60^{\circ} \rightarrow \sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2} ; 90^{\circ} \rightarrow \sqrt{\frac{4}{4}}=1\).

This gives the values of sine for these five angles.

Now for the remaining three, use:\(\sin \left(180^{\circ}-x\right)= \sin x \quad \sin \left(180^{\circ}+x\right)=\,- \sin x \sin \left(360^{\circ}-x\right)=\,- \sin x\)This means, \(\sin \left(180^{\circ}-0^{\circ}\right)=\sin 0^{\circ} \quad \sin \left(180^{\circ}+90^{\circ}\right)=\,- \sin 90^{\circ} \sin \left(360^{\circ}-0^{\circ}\right)=\,- \sin 0^{\circ}\)

Step 3: Determine the value of \(\cos\).\( \sin \left(90^{\circ}-x\right)=\cos x\)To find values for \( \cos x\), use this formula.For example, equals \(\left(90^{\circ}-45^{\circ}\right)= \sin 45^{\circ},\left(90^{\circ}-30^{\circ}\right)=\sin 60^{\circ}\) and vice versa.You can quickly determine the value of the \(\cos\) function by using this method:

Step 4: Determine the value of \(\tan\). We know that \(\sin\) divided by \(\cos\) equals the \(\tan\).\(\frac{{\sin }}{{\cos }} = \tan \)Divide the value of \(\sin\) at \(0^{\circ}\) by the value of \(\cos\) at \(0^{\circ}\) to get the value of \(\tan\) at \(0^{\circ}\). Take a look at the sample below.\( \tan 0^{\circ}=\frac{0}{1}=0\)In the same way, the table would be as follows.

Step 5: Determine the value of \(\cot\).The reciprocal of \(\tan\) is equal to the value of \(\cot\). Divide \(1\) by the value of \(\tan\) at \(0^{\circ}\) to get the value of \(\cot\) at \(0^{\circ}\). So, \(\cot 0^{\circ}=\frac{1}{0}=\infty\) or Not Defined will be the value.In the same way, a \(cot\) table is provided below.

Step 6: Determine the value of \(\operatorname{cosec}\).The reciprocal of \(\sin\) at \(0^{\circ}\) is the value of \({\text{cosec}}\).\(\operatorname{cosec} 0^{\circ}=\frac{1}{0}=\infty\) or Not Defined \(\operatorname{cosec} 0^{\circ}=\frac{1}{0}=\infty\) or Not DefinedIn the same way, a table for cosec is provided below.

Step 7: Determine the value of \(\mathrm{sec}\).All reciprocal values of \(\cos\) can be used to calculate the value of \(\sec\). The value of \(\sec\) on \(0^{\circ}\) is the inverse of the value of \(\cos\) on \(0^{\circ}\). As a result, the value will be \(\sec 0^{\circ}=\frac{1}{1}=1\).

Similarly, the table for a sec is shown below.

Hence, the required trigonometric table for all the trigonometric ratios is as follows

Practice Exam QuestionsTricks to Remember Trigonometry Table

The trigonometry table can be useful in a variety of situations, and it is simple to remember. Remembering the trigonometric table is simple if you know the trigonometry table formula and trigonometry table trick, as trigonometry formulas are used to create the trigonometry ratios table.

Let’s learn how to recall the trigo table with just one hand! As illustrated in the image, give each finger the standard angles. We will count our fingers while filling the sine table, but we will just fill the data in reverse order for the cos table.

1st Step: To calculate the standard angle for the sine table, count the fingers on the left side.

2nd Step: Divide the number of fingers by four.

3rd Step: Take out the square root of the ratio.

Example 1: Because there are no fingers on the left side for \(\sin 0^{\circ}\), we will use \(0\). We obtain \(0\) when we divide zero by four. We may determine the value of \(\sin 0^{\circ}=0\) by taking the square root of the ratio.

Example 2: On the left-hand side, there are three fingers for \(\sin 60^{\circ}\). We obtain \(\left(\frac{3}{4}\right)\) when we divide \(3\) by \(4\). We may determine the value of \(\sin 30^{\circ}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\) by taking the square root of the ratio \(\left(\frac{3}{4}\right)\).

Similarly, we may fill the table with values for \(\sin 30^{\circ}, 45^{\circ}\), and \(90^{\circ}\).