Calculating trigonometric functions like tangent inverse (tan inverse) can be a tedious task, especially without the assistance of calculators or computers. However, one effective method of finding the tan inverse value is by utilizing a log table. In this article, we will explore this method step by step, making it easier for you to determine the tan inverse of any given angle.
Step 1: Understand the Log Table
Firstly, it is essential to familiarize yourself with the structure and format of a log table. A log table consists of two columns: one for the logarithm of numbers, and the other for the corresponding antilogarithm (exponential) values. The logarithms are usually found on the left side, and the antilogarithms on the right side of the table.
Step 2: Identify the Decimal Part
When finding the tan inverse value using a log table, the first step is to determine the decimal part of the angle. For example, if you want to find the tan inverse of 1.23, the decimal part is 0.23.
Step 3: Locate the Logarithm Value
Now that you have the decimal part, locate the corresponding logarithm value in your log table. If the decimal part is not listed directly, find the closest value that is less than your decimal. In our example, the logarithm value of 0.23 would be 0.3617.
Step 4: Find the Angle
The next step is to use the logarithm value to determine the angle. Look for the same logarithm value in the column for antilogarithms and find the corresponding angle. In this case, the angle corresponding to the logarithm value of 0.3617 is 20°.
Step 5: Account for the Integer Part
Remember that the previous steps only considered the decimal part of the angle. Now, it’s time to calculate the tan inverse value taking into account the integer part. In our example, with the angle of 20°, we need to add the integer part (1 in this case) to get the final tan inverse value.
How to find tan inverse value using log table?
To find the tan inverse value using a log table, you need to follow these steps:
1. Identify the decimal part of the angle.
2. Locate the corresponding logarithm value in the log table.
3. Find the angle associated with the logarithm value from the antilogarithm column.
4. Account for the integer part of the angle.
5. Add the integer part to the angle obtained from the log table to find the final tan inverse value.
FAQs:
Q1: What is a log table?
A1: A log table is a mathematical table that provides the logarithms and antilogarithms of numbers.
Q2: How can a log table be helpful in finding the tan inverse?
A2: A log table allows us to find the angle associated with a logarithm value, which is useful in determining the tan inverse value.
Q3: Are log tables still used today?
A3: Although log tables have become less common nowadays due to the availability of calculators and computers, they can still be useful in certain situations.
Q4: Can I use a calculator instead of a log table?
A4: Yes, calculators provide convenient ways to find the tan inverse value directly without using a log table.
Q5: What if the decimal part is not listed in the log table?
A5: In such cases, find the closest value in the table that is less than your decimal part.
Q6: How accurate are log tables?
A6: Log tables are accurate within their precision limits but may introduce some rounding errors.
Q7: Can log tables be used for all trigonometric functions?
A7: Yes, log tables can be used to find the inverse values for other trigonometric functions like sine and cosine as well.
Q8: Do all log tables have the same format?
A8: No, different log tables may have variations in formatting, but the basic structure remains the same.
Q9: Can log tables be used for negative angles?
A9: Log tables are designed to work with positive angles only. For negative angles, additional calculations are required.
Q10: Why is it necessary to consider the integer part separately?
A10: Considering the integer part is important as it determines the quadrant the angle is in.
Q11: Is it possible to find the precise tan inverse value using a log table?
A11: Log tables provide approximate values, so if you need a precise value, other methods like a calculator should be used.
Q12: Are there online log tables available?
A12: Yes, some websites offer digital log tables that can be used for quick access and ease of use.