An examination of the table of natural functions will indicate in the column at the left, angles of 0 degrees to and including 45 degrees, reading down. The column to the extreme right will be found to contain degrees from 45-90 inclusive, reading up.

This compact arrangement of table is made possible thru the fact that sines and cosines, tangents and cotangents are reciprocals one of the other. That is, as the sine (column 2, reading down) increases in value, the cosine of the complementary angle (columns 6 and 2, reading up) decreases.

## Example 1

Find the value of the sine of 40 degrees.

Solution - Columns 1 and 2, reading down, sin 40 degrees = .6428.

## Example 2

Find the value of sin 50 degrees.

Solution - Columns 6 and 5, reading up, sin 50 degrees = .7660.

## Example 3

Find the value of cos 40 degrees.

Solution - Columns 1 and 5, reading down, cos 40 degrees = .7660 (which is as might have been expected. Since 40 degrees is the complement of 50 degrees, the cos 40 degrees should be the same in value as the sin 50 degrees.

Example 4- - Find the value of cos 87 degrees.

Solution - Columns 6 and 2 reading up, cos 87 degrees = .0523

## Example 5

Tangent and cotangent values. Proceed as with sines using columns 1 and 3, reading down, for tangent values between 0-45 degrees inclusive, columns 6 and 4, reading up, for values between 45-90 degrees.

For cotangent values between 0-45 degrees use columns 1 and 4 reading down, and columns 6 and 3 reading up for cotangent values between 45-90 degrees inclusive.

## Example 6

sin = . 5150, find the angle.

Solution - Looking in columns 2 and 5 (sine values from 0-90 degrees) Ans.

31 degrees (Columns 2 and 1). Example 7. - cot = 1.3764, find the angle. Solution - Looking in columns 3 and 4, Ans. = 36 degrees.