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8. Method of using trigonometric table

We have learnt how to determine the trigonometry ratios for the angle

$0^{\circ}$ ,

$30^{\circ}$ ,

$45^{\circ}$ ,

$60^{\circ}$ and

$90^{\circ}$ .

Now let us learn how to calculate the trigonometric ratios of all the other acute angles using the trigonometric tables.

$1^{\circ}$

$=$

$60$ minutes. It is denoted by

${60}'$ .

${1}'$

$=$

$60$ seconds. It is denoted by

${60}''$

The trigonometric tables provide values, correct to four decimal places, for angles ranging from

$0°$ to

$90°$ and spaced at

${60}′$ intervals. A trigonometric table is made up of three parts.

A column on the far left with degrees ranging from

$0°$ to

$90°$ , followed by ten columns labelled

${0}'$ ,

${6}'$ ,

${12}'$ ,

${18}'$ ,

${24}'$ ,

${30}'$ ,

${36}'$ ,

${42}'$ ,

${48}'$ , and

${54}'$ .

Five columns under the head mean difference has values from

$1$ ,

$2$ ,

$3$ ,

$4$ and

$5$ .

The appropriate adjustment is obtained from the mean difference columns for angles containing other measures of minutes (other than

${0}'$ ,

${6}'$ ,

${12}'$ ,

${18}'$ ,

${24}'$ ,

${30}'$ ,

${36}'$ ,

${42}'$ ,

${48}'$ , and

${54}'$ ).

The mean difference is added in the case of sine and tangent but subtracted in the case of cosine.

Trigonometric Table:

Trigonometry table.pdf

1. Find the value of

$\sin 74^{\circ}{39}'$ .

Example:

Solution:

First, rewrite the given sine value as follows:

$\sin 74^{\circ}{39}'$

$=$

$\sin 74^{\circ}{36}'$

$+$

${3}'$

Find the value of

$\sin 74^{\circ}{36}'$ from the natural sine table by doing the following step.

Check for

$74^{\circ}$ in the extreme left column and

${36}'$ in the top row, the decimal value intersecting the corresponding column and row is the required value of

$\sin 74^{\circ}{36}'$ .

$\Rightarrow \sin 74^{\circ}{36}'$

$=$

$0.9641$

The value corresponding to

$3$ in the mean difference column gives the value of

${3}'$ , which is to be added to the ten thousandth place of the above-determined value.

$\Rightarrow {3}'$

$=$

$2$ .

Therefore, the required sine value is given by:

$\sin 74^{\circ}{39}'$

$=$

$\sin 74^{\circ}{36}'$

$+$

${3}'$

$=$

$0.9643$

2. Find the value of

$\cos 34^{\circ}{55}'$ .

Solution:

First, rewrite the given cosine value as follows:

$\cos 34^{\circ}{55}'$

$=$

$\cos 34^{\circ}{54}'$

$+$

${1}'$

Find the value of

$\cos 34^{\circ}{54}'$ from the natural cosine table by doing the following step.

Check for

$34^{\circ}$ in the extreme left column and

${54}'$ in the top row, the decimal value intersecting the corresponding column and row is the required value of

$\cos 34^{\circ}{54}'$ .

$\Rightarrow \cos 34^{\circ}{54}'$

$=$

$0.8202$

The value corresponding to

$1$ in the mean difference column gives the value of

${1}'$ , which is to be subtracted from the ten thousandth place of the above-determined value.

$\Rightarrow {1}'$

$=$

$2$ .

Therefore, the required cosine value is given by:

$\cos 34^{\circ}{54}'$

$=$

$\cos 34^{\circ}{54}'$

$+$

${1}'$

$=$

$0.8200$

Reference:

State Council of Educational Research and Training (2018). Mathematics. Term - III Volume 2: Chapter 3 Trigonometry(pg.79 - 84). Printed and Published by Tamil Nadu Textbook and Educational Services Corporation.

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8. Method of using trigonometric table

Theory: