NATURAL TANGENTS

HOW TO USE NATURAL TANGENTS CALCULATIONS WITH ILLUSTRATIONS

Method of using the table of  tangents : this table is also known as the table of natural tangents .At intervals of 60', we can find the values of sines and cosines of angles ranging from 0° to 89°.

         The table of natural tangents is essentially divided into the following sections, as shown by the following tables. 

        

       (i) the angles in the table's extreme left vertical column are from 0° to 89° at intervals of 1°. 

 

        (ii) at intervals of 6' , the horizontal row at the top of the chart is from 0' to 54'.

        (iii) at intervals of 1', the angles in the horizontal row at the top of the chart are from 1' to 5'.

               This portion of the chart is referred to as the mean difference column.

* Note: 

            we obtain the tangent value of a given angle from the chart, which is expressed in four decimal places. 

Solved examples using the table of natural tangents : 

         1. Find the value of tan 55°. 

Solution:   Find the value of sin 55° by the using the table of natural sines we need to go through the extreme left vertical column 0° to 89° and move downwards till we reach the angle 55°.               

               Then we move horizontally to the right at the top of the column headed by 0' (or 0.0°) and read the figure 1.4281, which is the require value of tan 55°. 

Therefore tan55° = 1.4281   .... Answer

      2. Find the value of tan 60°36’

Solution:  Find the value of tan 60°36’ by the using the table of natural tan we need to go through the extreme left vertical column 0° to 89° and move downwards till we reach the angle 60°. 

           Then we move horizontally to the right at the top of the column headed by 36' (or 0.6°) and read the figure 1.7747 , which is the require value of tan 60°36’ .

 Therefore tan 60°36’  = 1.7747 ... Answer

         3.Use tables to find tan72°60' 

Solution: Using the trigonometric table of natural tangents. tan 72°60' = tan ( 72° + 60') = tan (72°+ 1° ) = tan (71°)  Because 60' = 1°

Therefore  tan 70°60' = tan (71°)= 2.9042

 tan 72°60'= 2.9042     ... Answer

          4. Find the angle θ, tan θ = 1.4994

solution : tan θ = 1.4994

Therefore   θ = tan⁻¹ 1.4994 = 56°18′ because in the table, the value 1.4994 corresponds to the column of 18′ in the row of 56°.

θ = tan⁻¹ 1.4994 

    = 56°18′ or 56.3° .... Answer