how to use a log book to find natural sines and natural cos ?

Let’s understand it using an example.

Find value of tan28⁰36^/

Use the natural tangent table for this.

Step 1: first locate the 28˚ in first degrees column.

Step2: then, locate 36َ in next columns ranging from 0^/ to 54^/.

The coinciding point will give you the value of tan28⁰36^/ which is 0.5452.

Find the value of tan72⁰28^/

As there is no column of 28^/

We first find the value of tan72⁰28^/ and then add the mean difference of 4^/.

i.e. value of tan72⁰28^/ (follow above steps)

Now, add 4^/ value from mean difference column in 72˚ row i.e. 129.

The answer will be 3.1524 + 129 = 3.1653

In the similar way you can find the value of sine and cosine using natural sine and natural cosine tables.

Hope, this method is clear to you.

Best wishes!