One of fundamental fundamentals of the exact sciences is the concept about trigonometrical functions. They define the simple relations between the parties of a rectangular triangle. The sine belongs to family of these functions. To find it, knowing a corner, it is possible a large number of the ways including experimental, computing methods and also use of reference information.

## It is required to you

- - calculator;
- - computer;
- - spreadsheets;
- - tables of a bradis;
- - paper;
- - pencil.

## Instruction

1. Use the calculator with function of calculation of a sine for obtaining the necessary values on the basis of knowledge of a corner. Even the simplest devices have similar functionality today. At the same time calculations are made with very fine precision (as a rule, to eight and more signs after a comma).

2. Apply the software representing the environment for work with spreadsheets, started on the personal computer. Examples of similar applications are Microsoft Office of Excel and OpenOffice.org Calc. Enter the formula consisting of a call of function of calculation of a sine with the necessary argument into any cell. Press Enter. In a cell the required size will be displayed. Advantage of spreadsheets is the possibility of fast calculation of values of functions for a big set of arguments.

3. Learn approximate value of a sine of the angle from Bradis's tables if they are available. Their shortcoming is the accuracy of values limited to four signs after a comma.

4. Find approximate value of a sine of the angle, having made geometrical constructions. On the sheet of paper draw a piece. By means of a protractor postpone from it a corner which sine needs to be found. Draw one more piece crossing the first in some point. Perpendicular to the first piece draw the straight line crossing two already existing pieces. The rectangular triangle will turn out. Measure length of its hypotenuse and leg, opposite to the corner constructed by means of a protractor. Divide the second value into the first. It will also be required size.

5. Calculate a sine of the angle, using decomposition in a row of Taylor. If the value of a corner is presented in degrees, transfer it to radians. Use a look formula: sin (x) = x - (х^3)/3! + (х^5)/5! - (х^7)/7! + (х^9)/9!-... For increase in speed of calculations write down the current value of numerator and a denominator of the last member of a row, making calculation of the following value on the basis of previous. Increase row length for obtaining more exact size.