Trigonometry is one of the most important sections of algebra and geometry for study in high school. This science originates from the time of ancient Greece. In the Middle Ages, the countries of the Middle East, as well as India, made the most significant contribution to the study and application of trigonometry.
Often, in the process of studying new material, students experience difficulties in understanding the new terminology, especially if it is not connected in any way with previously acquired knowledge. However, it is important to realize the importance of mastering the basic foundations of any topic, because the success of further education of a child depends on this, in the first place. In this article, we will consider such a trigonometric term as the sin of the angle from which, we can say, all trigonometry begins.
Definition
Consider the geometric meaning of this function.
To determine the sine , the aspect ratio of the right triangle is used. Let's consider in more detail. Sin is the ratio of the opposite side to the hypotenuse of such a triangle.
For easier understanding, explain the definition using an auxiliary drawing:
Applying the terms already passed in geometry, we denote the hypotenuse AB by the small Latin letter c, and the legs of the right triangle AC and BC are taken as b and a, respectively. Thus, considering the angle A, its sin is the ratio of a to c. Now consider another, paired with an acute angle B. Its sin is the ratio of b to c.
Now consider the algebraic meaning.
If we consider the term "sine" from the point of view of this section of mathematics, then we should turn to the Cartesian coordinate system. It will take a unit circle (whose radius is equal to one arbitrary unit) centered at the origin.
We postpone a certain angle equal to alpha from the abscissa axis. The second ray, forming a given angle, intersects the unit circle at point A. We will need it, namely its second coordinate. Its value is numerically equal to the sine of the deferred angle.
Scopes and Values
We recall the general case. The domain of definition for a function is usually denoted as D (f), and it is located along the abscissa. In turn, the range of permissible values is denoted as E (f), and it should be found along the ordinate axis.
In our case. For the sine, its range of permissible values is on the interval from -1 to 1, and all real numbers belong to the definition domain. We also note that the sine function is periodic, and its period is pi.
Conclusion
Now you can answer all questions related to the definition of a sin angle without a doubt, including: sin is the relation of what to what, how it is located. We hope that this article was useful and understandable for you.