# S.L. Loney Tables of Logarithms Solutions (Chapter 11)

SL Loney Plane Trigonometry Solutions for Chapter 11 ‘Tables of Logarithms and Trigonometrical Ratios’ is an important chapter to have an in-depth understanding of the log table and its applications in mathematical calculations. Deeply ingrained understanding is important for you to prepare for challenging competitive exams like JEE, NTSE, and the Olympiad of Mathematics. The main topics of this chapter include logarithms, antilogs, logarithmic functions, logs of trigonometric ratios, and proportional parts.

SL Loney Plane Trigonometry Solutions for Tables of Logarithms and Trigonometrical Ratioshas a total of 13 exercise-based questions and 10 additional solved examples. In this chapter, you will learn the simplest ways to find the value of the logarithmic equation by using a log graph. You will get to know about the chamber’s mathematical table for logarithms of all numbers from 1 to 108000, types, and values of the trigonometric ratios of angles between 0^{0} and 45^{0} as well as the steps of using a log table. You will get to know about the table of logarithm sine and cosines.

SL Loney Trigonometry solutions book provides absolute answers to difficult problems that have been carefully developed by our team of mathematics professionals to enable you to achieve in-depth knowledge of all areas of trigonometry. You’re going to be able to improve your supercomputing skills and learn concepts rather than just mugging up some methodologies. The whole book is among the most famous in standard text collection dealing with trigonometry.

## Important topics for SL Loney Plane Trigonometry Solutions Chapter 11: Tables of Logarithms and Trigonometrical Ratios

In mathematics, the logarithm table can be used to calculate the significance value of the logarithm equation. The best way to find the value of the logarithmic equation is to use the log table. Here the definition of the logarithmic function and the procedure for using the logarithm table is discussed in detail.

**Antilog Definition**: An antilog, also recognized as “Anti-Logarithms,” of a number, is the equal and opposite technique of figuring a logarithm of the same number. Remember, if x is the logarithm of a number y with base b, perhaps we can assume that y is the antilog of x to base b. It shall be specified by

- If log
_{b}y = x - Then, y = antilog x

**Description of the Logarithmic Function:**

The logarithmic function is known as an inverse exponential curve. The logarithmic function is seen as follows:

Such as x, a > 0, and a (1) and also,

**y= log _{a }x, if x = a^{y}**

At this time, the logarithmic function is written as:

** f(x) = log _{a }x**

- The two most famous bases used during logarithmic functions are base e and base 10. The log function with base 10 is considered the typical logarithmic function and is represented by log10 or simply log, i.e.,
**f(x) = log**_{10}

- The log function at base e is considered the natural logarithmic function and is represented by the log symbol.

**f(x) = log _{e} x**

**To calculate a logarithm for a number**, we may use the logarithm table regardless of using a simple formula. Before we consider the logarithm of value, we will learn the properties and the mantissa component of value.

**Tables of Trigonometric Ratios:**

- Tables displaying the values of the trigonometric ratios of angels (0
^{0}and 45 °), angle, the angles by variations of 1′ are included in the chamber tables. - The ratios of angles between 45
^{0}and 90^{0}degrees must be tabulated separately, as the ratios of angles between 45^{0}and 90^{0}degrees may be compared to those of angles between 0^{0}and 45^{0}For example sin 76^{0}11’ = sin (90^{o}-13^{0}49’) = cos13^{0}49’ - This table is called a table of natural sines, cosines, etc. to distinguish it from the table of logarithmic sines, cosines, etc.
- If anyone tries to find the sine of an angle that includes an integral number of degrees and minutes, he may get it from the tables, although the angle comprises the second angle, we will use the principle of equal portions.

**Chamber’s Mathematical Table**: A table is a collection of statistics and figures ordered in columns and sections. It’s a really helpful way to arrange numerical details or results.

**Table of Logarithmic Sines and Cosines:**

**Sine and Cosine — sin (θ) and cos(θ):**They are constants that show the form of the right triangle. The ratio of the contrary direction to the hypotenuse, while the ratio of the neighbouring side to the hypotenuse, is the ratio of the corresponding side to the hypotenuse, looking out from the vertex with the angle Δ.- In certain kinds of trigonometric equations, as in the triangle solution, we also need trigonometric ratio logarithms. To prevent the difficulty of first extracting the sine of some angle from the tables and then getting the logarithm of this sine by the second application of the tables, it was considered convenient to provide separate tables providing the logarithm of various trigonometric functions of angles.
- Although the sine of the angle is often less than equality, the logarithm from its sine is indeed negative.

### Discussion of Exercises of SL Loney Plane Trigonometry Solutions Chapter 11: Tables of Logarithms and Trigonometrical Ratios

- The first array of exercise-based questions consists of a total of 13 questions which are the mixture of problem-based and theoretical questions.
- Problem-based questions can help you grasp the fundamental methods of using a log table to solve complicated mathematical equations and as quickly as possible. You will learn to use the chamber’s mathematical tables.
- Theoretical questions are based on the concept of trigonometric ratios and table of natural sine, cosines, etc. You will get to know about the characteristics, mantissa, and antilogarithms.

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