How to use the Bradis table: detailed instructions
📌 Brief answer: To find the value of sin, cos, tan, or cot for an angle that is not in the table, take the nearest tabular value and add (or subtract) the correction for the difference in minutes (1′, 2′, or 3′). Corrections are indicated in the last columns of the table. For sine and tangent, the correction is added; for cosine and cotangent, it is subtracted.
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How to correctly use the Bradis table: step-by-step instructions
The Bradis table presents the values of angles that are multiples of 6 minutes (0′, 6′, 12′, etc.). If you need to find the values of sine, cosine, tangent, or cotangent of an angle that is not in the table, you should choose the value closest to it and add (subtract) the correction corresponding to the difference of 1′, 2′, or 3′.
- Determine the function. For sine and cosine — one table, for tangent and cotangent — another.
- Find the degrees. In the left column, find the row with the required number of degrees.
- Find the minutes. In the top row, find the column with the minutes (0′, 6′, 12′ … 60′).
- Take the value. At the intersection of the row and column — the tabular value.
- Apply the correction. If the angle is not a multiple of 6′, take the correction from the last three columns.
Important to remember:
- For sine and tangent, the correction is added to the tabular value.
- For cosine and cotangent, the correction is subtracted from the tabular value.
How to use the Bradis table for sines: examples
Example 1: Finding sin(8°19′)
Problem. Find sin(8°19′). This value is not in the table. Take the nearest value from the table — 8°18′ (from the table: sin(8°18′) = 0.1444).
To find sin(8°19′), let's use the correction table. sin(8°18′) and sin(8°19′) differ by one minute (1′) upward. So we take the correction value for 1 minute, which from the table is 3. This means that we need to add 0.0003 to the value 0.1444. We get 0.1447.
Answer. sin(8°19′) = 0.1447.
Example 2: Finding sin(8°23′)
Similarly, we can get the value for sin(8°23′). Here the nearest value in the Bradis table to 23′ is 24′, that is, we need to reduce the value of sin(8°24′) by the correction value (since 23 < 24).
We get: sin(8°24′) = 0.1461, then sin(8°23′) = 0.1461 − 0.0003 = 0.1458, since the correction value for 1′, by which we must reduce the value, is 3.
Answer. sin(8°23′) = 0.1458.
Example 3: Finding sin(30°10′)
The nearest tabular value is 30°12′ (sin = 0.5030). The difference is 2′ downward, so the correction is subtracted: 0.5030 − 0.0006 = 0.5024.
Answer. sin(30°10′) = 0.5024.
How to use the Bradis table for cosines: examples
For cosine, the same rule applies, but with one important difference: the correction is subtracted, not added. This is because the cosine decreases as the angle increases.
Example 1: Finding cos(15°25′)
The nearest tabular value is 15°24′ (cos 15°24′ = 0.9641). The angle 15°25′ is greater by 1′, so we subtract the correction: 0.9641 − 0.0001 = 0.9640.
Answer. cos(15°25′) = 0.9640.
Example 2: Finding cos(15°28′)
The nearest tabular value is 15°30′ (cos 15°30′ = 0.9636). The angle 15°28′ is smaller by 2′, so we add the correction: 0.9636 + 0.0002 = 0.9638.
Answer. cos(15°28′) = 0.9638.
Example 3: Finding cos(60°10′)
The nearest tabular value is 60°12′ (cos = 0.4970). The difference is 2′ downward, so we add the correction: 0.4970 + 0.0003 = 0.4973.
Answer. cos(60°10′) = 0.4973.
How to use the Bradis table for tangent and cotangent
For tangent and cotangent, corrections work the same way as for sine and cosine, but the numerical values of the corrections are different and grow significantly as the angle increases.
Example 1: Finding tan(24°10′)
The nearest tabular value is 24°12′ (tan = 0.4494). The angle 24°10′ is smaller by 2′, so we subtract the correction: 0.4494 − 0.0007 = 0.4487.
Answer. tan(24°10′) = 0.4487.
Example 2: Finding tan(45°)
The value is tabular, no correction needed: tan 45° = 1.0000.
Example 3: Finding cot(30°)
Tabular value: cot 30° = 1.7321.
Example 4: Finding tan(50°15′)
The nearest tabular value is 50°12′ (tan = 1.2002). The difference is 3′ upward, so we add the correction: 1.2002 + 0.0026 = 1.2028.
Answer. tan(50°15′) = 1.2028.
Correction table for sine and cosine
Corrections depend on the angle. For small angles (0°–15°) they are one value, for large ones — another. Below is a reference table for the most common cases.
| Difference (minutes) | Correction (small angles) | Correction (large angles) |
|---|---|---|
| 1′ | 0.0003 | 0.0001 |
| 2′ | 0.0006 | 0.0002 |
| 3′ | 0.0009 | 0.0003 |
Note: the exact values of the corrections are indicated in the last columns of the Bradis table for a specific angle. Here averaged examples are given.
How to use the Bradis table in 9th grade
In 9th grade, the Bradis table is used when studying trigonometry and solving geometry problems. It is important for students not only to be able to find values, but also to understand how to work with minutes and corrections.
What is most often needed in 9th grade:
- finding the values of sin, cos, tan, cot for angles from 0° to 90°;
- solving right triangles (by side and angle);
- application of reduction formulas for angles greater than 90°;
- preparation for the OGE — tasks with trigonometry in the geometry section.
More about the table: Complete Bradis table.
About the accuracy of calculations
If you compare the values of sin and cos with the values calculated on a calculator, you can sometimes see discrepancies. Such errors are quite acceptable when calculating from the table.
For more on tables, see the section Bradis table.
Frequently asked questions
How do you correctly use the Bradis table?
How do you use the Bradis table for cosines?
How do you work with corrections in the Bradis table?
What if the angle is greater than 90°?
How accurate are the values in the Bradis table?
📚 See also:
Compiled by: Alexey Pavlov, mathematics teacher.
Source: classic four-digit tables by V. M. Bradis (1921) in modern edition.
Last updated: 11.10.2026.
