The straight line having one general point with a circle is a tangent to a circle. Other feature of a tangent – it is always perpendicular to the radius which is carried out to a contact point, that is the tangent and radius form a right angle. If from one point And two tangents to a circle of AV and the EXPERT are carried out, then they are always equal among themselves. Definition of a corner between tangents (AVS corner) is made by means of Pythagorean theorem.
Instruction
1. For definition of a corner it is necessary to know the radius of a circle of OV and OS and distance of a point of the beginning of a tangent from the center of a circle - O. Itak, corners of ABO and ACO are equal 90 degrees, OV radius, for example 10 cm, and the distance to the center of a circle of the joint-stock company is equal to 15 cm. Determine tangent length by a formula according to Pythagorean theorem: AV = a square root from AO2 – OB2 or 152 - 102 = 225 – 100 = 125;
2. Take a square root. 11.18 cm will turn out. As the corner of VAO represents sin or the relation of the parties IN and the joint-stock company calculate its value: VAO corner Sin = 10: 15 = 0.66
3. Then, using the table of sine, find this value which corresponds to about 42 degrees. The table of sine is used for the solution of various tasks – physical, mathematical or engineering. It is necessary to find out the size of a corner YOU for what it is necessary to double the size of this corner, that is, about 84 degrees will turn out.
4. The size of the central corner corresponds to the angular size of an arch on which it relies. The size of a corner can also be determined by a protractor, having put it to the drawing. As similar calculations belong to trigonometry, it is possible to use a trigonometrical circle. With its help it is possible to transfer degrees to radians and vice versa.
5. It is known that the cycle makes 360 degrees or 2P a radian. On a trigonometrical circle values of sine and cosines of the main corners are displayed. It is worth reminding that the value of a sine is on axis Y, and a cosine on axis X. Values of a sine and a cosine are in an interval from-1 to 1.
6. It is possible to define values of a tangent and a cotangent of a corner having divided a sine into a cosine, and a cotangent on the contrary – a cosine on a sine. The trigonometrical circle allows to define signs of all trigonometrical functions. So, the sine is an odd function, and a cosine – even. The trigonometrical circle allows to understand that a sine and a cosine – periodic functions. It is known that the period is equal 2P.