Trigonometric tables

Trigonometric Ratios from Tables

Trigonometric ratios (sine, cosine, and tangent) of angles can be found using trigonometric tables, just like we use logarithmic tables to find logarithms.

To read from a trigonometric table:

1. The degrees of the angle are listed in the first column on the left.
2. The minutes (') are listed across the top row.
3. Find the intersection of the row for the degree and the column for the minutes to get the trigonometric value.

If the angle has zero minutes, read the value under the column labeled 0'.

Example 1: Find sin 56°00'

1. Go to the row labeled 56° in the leftmost column.
2. Then move across to the column labeled 0'.
3. From the table: sin 56°00' = 0.8290

Example 2: Find cos 78°45'

1. First, find cos 78°42', since your table might not have 45' directly.
   • From the row labeled 78°, and column 42', you find cos 78°42' = 0.1959
2. Now calculate the value for the remaining 3 minutes (45' - 42') using the difference column (sometimes called the "mean difference" column).
   • From the difference column for 3', you find a value of 9, which is 0.0009
3. Since we are dealing with cosine, and the instructions for the table say to subtract the difference:
   • cos 78°45' = 0.1959 - 0.0009 = 0.1950

Note: Always check if the difference is to be added or subtracted. Usually:

1. Subtract for cosine
2. Add for sine and tangent