Each of us many hours spent on the solution of a problem in geometry.Of course, the question arises, why do you need to learn math?The issue is particularly relevant for the geometry, the knowledge that if they come in handy, it is very rare.But mathematicians have an appointment and for those who are not going to become an employee of the exact sciences.It causes a person to work and develop.
initial appointment of mathematics was not empowering students knowledge about the subject.Teachers set a goal to teach children to think, to reason, analyze and argue.This is what we find in the geometry with its numerous axioms and theorems, investigation and evidence.
cosine
Along with trigonometric functions and algebra inequalities are beginning to explore the corners of their value and finding.Cosine is one of the first formula that links the student to understand both sides of mathematics.
To find the other two sides and the angle between the cosine theorem applies.For a triangle with a right angle we approach and the Pythagorean theorem, but if we talk about an arbitrary figure, it is applied can not be.
cosine as follows:
AS 2 = AB 2+ Sun 2 2 * AB * Sun * cos & lt; ABC
square of one side is equal to the sum of the other two sides, taken in the square, minus their product multiplied by twoand the cosine of the angle formed by them.
If you look more closely, this formula is reminiscent of the Pythagorean theorem.Indeed, if we take the angle between the legs of equal to 90, then the value of its cosine is 0. As a result, there will be only the sum of the squares of the sides that reflects the Pythagorean theorem.
cosine Proof
From this expression we deduce the formula AS 2 and get:
AC 2 = BC 2 + AB 2 - 2 * AB * Sun * cos & lt; ABC
Thus, we seethat expression corresponds to the above formula, a testament to its truth.We can say that the cosine theorem proved.It is used for all types of triangles.
use
Besides lessons in mathematics and physics, this theorem is widely used in architecture and construction, to calculate the necessary aspects and angles.With its help determine the appropriate size and quantity of construction materials that will be needed for its construction.Of course, most of the processes that previously required human intervention and immediate knowledge, automated today.There are many programs that allow you to model such projects on the computer.Their programming is also carried out with all the mathematical laws, properties and formulas.
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