Tables of values of the trigonometric functions

The usual practice of obtaining the trigonometric functions of a given angle is to compute the trigonometric functions for many angles between 0° and 90° by more accurate methods and to compile these results in the form of a table to which the student may refer.

This table consists of angles from 0° to 45° listed by tenths of a degree in the left-hand column, reading downwards, and angles from 45° to 90° listed by tenths of a degree in the right-hand column, reading upwards. The angles horizontal­ly opposite each other are complementary. For example, the angle 3° on the left has opposite it the angle 87°. In the four columns between are the sinus, the cosines, the tangents, and the cotangents of these two angles. The same numbers have been used for functions of each of the two complementary angles, for as was shown the functions of an angle are equal to the co-functions of its complement.; For the angles on the left, the trigonometric headings at the top of the table indi­cate the column in which each function may be found.

In general, the tables of trigonometric functions are used for one of the purposes:

1. to find the functional value when the angle is known;

2. to find the angle when the functional value is known.

Exercises

1. Read the following words paying attention to the pronun­ciation :

tangent, practice, angle, cotangent, accurate, inaccurate, opposite, table, compile, sine, cosine.

2. Add the suffixes and translate the words:

-ward(s): up, after, down, to;

-ly: usual, horizontal, accurate, equal, general.

3. Make up sentences of your own using the words and ex­pressions given below:

method for obtaining, of a given angle, opposite, opposite each other, to compute the function.

4. Answer the following questions:

1. How do we obtain a trigonometric function of a given angle? 2. Of what angles does the list of trigonometric func­tions consist? 3. What indicates the column in which each function may be found?

5. Translate into Russian:

We have already discussed several methods for obtaining the trigonometric functions of a given angle. However, all the methods taken up were either inaccurate or restricted to special angles. Consequently, the usual practice is to com­pute the trigonometric functions for many angles between 0° and 90° by more accurate methods and to compile these results in a form of a table to which the student may refer.

6. Translate into English:

Для получения тригонометрической функции данного угла, надо вычислить тригонометрические функции для многих углов от 0° до 90° и составить таблицу.

Таблицы тригонометрических функций используются для нахождения величины функции, когда известен угол и для нахождения угла, когда известна величина функции.

TEXT

REVIEW

The trigonometric functions of an angle considered as certain ratios which were defined after placing the angle in standard positions on a rectangular coordinate system.

There are only a few angles for which the trigonometric functions can be found by geometrical considerations, and, therefore, tables must be used from which the values of the trigonometric functions of angles between 0° and 45°, but a few theorems about trigonometric functions of complementary and related angles permit us to find from these tables the functions of any angle.

One of the most important applications of the trigonomet­ric functions is the solution of right triangles.

Two-other topics discussed are particularly worth men­tioning.¹ The first is the" possibility of measuring an angle in different units; and the examination of the, two most fre­quently used units; the degree and the radian. The second topic is the interpolation between two values given in a table, which is not only used for trigonometric tables but in all cases .where numerical tables are used and values have to be found which are between two values in the table.

Note:

¹ are particularly worth mentioning — стоит упомянуть отдельно о