Finding tan Value from Trigonometric Table

We know the values of the trigonometric ratios of some standard angles, viz, 0°, 30°, 45°, 60° and 90°. While applying the concept of trigonometric ratios in solving the problems of heights and distances, we may also require to use the values of trigonometric ratios of nonstandard angles, for example, sin 62°, sin 47° 45′, cos 83°, cos 41° 44′ and tan 39°. The approximate values, correct up to 4 decimal places, of natural sines, natural cosines and natural tangents of all angles lying between 0° and 90°, are available in trigonometric tables.

Reading Trigonometric Tables

Trigonometric tables consist of three parts.

(i) On the extreme left, there is a column containing 0 to 90 (in degrees).

(ii) The degree column is followed by ten columns with the headings

           0′, 6′, 12′, 18′, 24′, 30′, 36′, 42′, 48′ and 54′ or

           0.0°, 0.1°, 0.2°, 0.3°, 0.4°, 0.5°, 0.6°, 0.7°, 0.8° and 0.9°

(iii) After that, on the right, there are five columns known as mean difference columns with the headings 1′, 2′, 3′, 4′ and 5′.

Note: 60′ = 60 minutes = 1°.

Table of Natural Tangents, Trigonometric Table

1. Reading the values of tan 38°

To locate the value of tan 38°, look at the extreme left column. Start from the top and move downwards till you reach 38.

We want the value of tan 38°, i.e., tan 38° 0′. Now, move to the right in the row of 38 and reach the column of 0′.

We find 0.7813.

Therefore, tan 38° = 0.7813.

 

2. Reading the values of tan 38° 48′

To locate the value of tan 38° 48′, look at the extreme left column. Start from the top and move downwards till you reach 38.

Now, move to the right in the row of 38 and reach the column of 48′.

We find 8040 i.e., 0.8040

Therefore, tan 38° 48′ = 0.8040.


3. Reading the values of tan 38° 10′

To locate the value of tan 38° 10′, look at the extreme left column. Start from the top and move downwards till you reach 38.

Now, move to the right in the row of 38 and reach the column of 6′.

We find 7841 i.e., 0.7841

So, tan 38° 10′ = 0.7841 + mean difference for 4′

                      = 0.7841

                      +        19  [Addition, because tan 38° 10′ > tan 38° 6′]

                          0.7860

Therefore, tan 38° 10′ = 0.7860.


Conversely, if tan θ = 0.9228 then θ = tan 42° 42′ because in the table, the value 0.9228 corresponds to the column of 42′ in the row of 42, i.e., 42°.






10th Grade Math

From Finding tan Value from Trigonometric Table to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  2. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    Read More

  3. Tenths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 12:03 PM

    Tenth Place in Decimals
    The first place after the decimal point is tenths place which represents how many tenths are there in a number. Let us take a plane sheet which represents one whole. Now, divide the sheet into ten equ…

    Read More

  4. Representing Decimals on Number Line | Concept on Formation of Decimal

    Jul 20, 24 10:38 AM

    Representing decimals on number line shows the intervals between two integers which will help us to increase the basic concept on formation of decimal numbers.

    Read More

  5. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 20, 24 01:11 AM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More