The trigonometric tables give the values, correct to four places of decimals for the angles from 0° to 90° spaced at intervals of 60′ . A trigonometric table consists of three parts.

**Method of using Trigonometric Table**

We have learnt to calculate the trigonometric ratios
for angles 0°, 30°, 45°, 60° and 90°. But during certain situations we need to calculate
the trigonometric ratios of all the other acute angles. Hence we need to know the
method of using trigonometric tables.

One degree (1°) is divided into 60 minutes (60′) and
one minute (1′) is divided into 60 seconds ( 60′′ ) . Thus, 1° = 60′ and 1′ = 60′′.

The trigonometric
tables give the values, correct to four places of decimals for the angles from 0°
to 90° spaced at intervals of 60′ . A trigonometric table consists of
three parts.

A column
on the extreme left which contains degrees from 0° to 90°, followed by ten columns
headed by 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.

For angles
containing other measures of minutes (that is other than 0′
, 6′
, 12′
, 18′
, 24′
, 30′
, 36′
, 42′
, 48′
and 54′
), the appropriate adjustment is obtained from the mean difference columns.

The mean
difference is to be added in the case of sine and tangent while it is to be subtracted
in the case of cosine.

Now let us
understand the calculation of values of trigonometric angle from the following examples.

**Example 6.11**

Find the
value of sin 64º34′.

*Solution*

**Example 6.12**

Find the
value of cos19º59′

*Solution*

**Example 6.13**

Find the value of tan70º13′

*Solution*

**Example 6.14**

Find the value of (i) sin 38º36′ + tan12º12′ (ii) tan 60º25′ - cos 49º20′

*Solution*

(i) sin 38º36′ + tan12º12′

sin38º36′ = 0.6239

tan12º12′ = 0.2162

sin38º36′ + tan12º12′ = 0.8401

(ii) tan 60º25′ - cos 49º20′

tan60º25′ = 1.7603 + 0.0012 = 1.7615

cos 49º20′ = 0.6521 -
0.0004 = 0.6517

tan 60º25′ - cos 49º20′ =1.1098

**Example 6.15**

Find the value of θ if (i) sin θ = 0.9858 (ii) cos θ
= 0.7656

*Solution*

(i)
sin θ =
0.9858 = 0.9857 + 0.0001

From
the sine table 0.9857 = 80°18′

Mean
difference 1 = 2′

0.9858 = 80°20′

sin *θ* = 0.9858 = sin80°20′

* **θ** = *80°20′

(ii) cos
θ =
0.7656 = 0.7660 - 0.0004

From the
cosine table

0.7660 =
40°0′

Mean
difference 4 = 2′

0.7656 =
40°2′

cos θ =
0.7656 =
cos 40°2′

* *θ* *=*
*40°2′

**Example 6.16**

Find the
area of the right angled triangle with hypotenuse 5*cm* and one of the acute angle is 48°
30′

*Solution*

Observe the steps in your home. Measure the breadth and the height
of one step.

Enter it in the following picture and measure the angle (of elevation)
of that step.

(i) Compare the angles (of elevation) of different steps of same
height and same breadth and discuss your observation.

(ii) Sometimes few steps may not be of same height. Compare the angles
(of elevation) of different steps of those different heights and same breadth and
dicuss your observation.

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9th Maths : UNIT 6 : Trigonometry : Method of using Trigonometric Table |

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