Trigonometric identities are called the series of relationships or equalities that exist between trigonometric functions. It is, by definition, valid for the values of the angles involved in the operation. There is a group of basic identities, which are often used in the simplest trigonometric functions; From these, and with the use of other identities, you can find up to 24 more equations, which will be applied according to the incognito raised.
With just two identities, and depending on five others, you can create a table with about 36 more formulas.
Trigonometry is the field of mathematics that is responsible for studying trigonometric proportions, such as: sine, cosine; tangent, cotangent; secant and cosecant Trigonometric functions, on the other hand, were conceived to, in some way, extend the value of ratios to real and complex numbers; this would normally be defined as the quotient of two sides of a triangle, which in turn are related to the angle of the triangle. There are only 6 trigonometric functions.
Identities, on the other hand, only establish the existing equalities between the trigonometric functions used. In general, this applies to geometry, astronomy, physics, and cartography.
In addition to the basic identities, you can find the multiple angle identities, with the expression: cos (nx) = Tn (cos (x)). Also, the identities of the double, triple and average angles and the identities of the reduction of exponents can be applied in certain problems. These operations, it should be noted, also involve other elements present in geometric figures, such as data relating to the legs.
Before we start looking at the different trigonometric identities, we must know some terms that we will use a lot in trigonometry, which are the three most important functions within it. The cosine of the angle of a right triangle or rectangle is defined as the correlation between the adjacent leg and the hypotenuse:
Another function that we will use in trigonometry is “senol”. We will define sine as the relationship between the opposite leg and the hypotenuse in a right triangle:
Meanwhile, the word tangent in math can have multiple different meanings. However, trigonometry has been responsible for defining it as the relationship between the legs of a right triangle, the same as saying that it is the numerical value resulting from dividing the length of the opposite leg by that of the leg adjacent to the angle.
