can u tell hw to use natural tangents in logarithmic tables book

In the above a table is shown of natural tangents. Suppose we need to find the tan of 28^{0}56’

We will do the following steps:

- From the table we try to find the nearest value given to 28
^{0}56’. For this we move to table with row 28. Shown by the red rectangle. - Then we find out the minute nearest to 56’ so we search the column nearest to 56’. We get 54’ to be the nearest (shown by blue rectangle).

So we get a value of the angle 28^{0}54’ which is equal to 5520. The decimal point before 5520 is understood.

3. Then we find the difference of the actual value and 28^{0}54’, 28^{0}56’- 28^{0}54’= 2’.

4. Then we find the mean difference for 2’. From table of mean difference we get (shown by yellow rectangle) to be 8.

5. To get the value of tan 28^{0}56’ we add 5520 to the mean difference 8

5520 + 8 = 5528.

Recalling the decimal before 5528 we have our final value:

So tan(28^{0}56’) =** 0.5528.**

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