Trigonometry is one of the major branches of Mathematics which deals with the relationship between the lengths and angles of triangles. Students can learn the basics of trigonometry in their high school classes. For the purpose of computations in astronomy about two thousand years ago, trigonometric tables were created. An important area of study which led to the development of the first mechanical computing devices is the calculation of mathematical tables.
In mathematics, the tables of trigonometric functions are useful in different areas such as integration and differentiation. Trigonometric tables were the essential tools for navigation, engineering and science before the existence of pocket calculators. Trigonometric tables have six different types of functions of trigonometry namely sine, cosine, tangent, secant, cosecant and cotangent. All these functions have different values for different angular values. These six functions can be displayed in relation to the right triangle.
The reason behind the development of trigonometry is to compute the angles and distances in different fields like map-making, artillery and so on. Besides, there are many other applications of trigonometry in real life situations also. For example, to find the length of the shadow, height of the tower, height of the hill etc., There exist different identities of trigonometry with different values of angles such as half-angle, double angle and composite angles. These identities are useful in solving problems related to trigonometry simplifications.
Trigonometric identities are defined as a set of equalities that involve the functions of trigonometry and those are true for each value of the possible variables in which both the sides of equality can be found. Geometrically, all these identities contain some functions of one or more angles. However these identities are useful in order to simplify the expressions which contain trigonometric terms.
The values of functions of trigonometry can be evaluated based on the trigonometry angles. Each angle possesses different values. All these values are dependent on the length of the sides and the measure of angles of that particular triangle. Hence, all these angles are used in different branches of mathematics such as geometry and calculus. In calculus, there are many formulas related to trigonometry. Among them, an important application can be given as the integration of certain functions other than trigonometry. Here, we can use the technique of substitution of trigonometric related functions. Then, we can simplify the obtained integral using the trigonometric identity.
The basic definitions of trigonometry are related to right triangles and those were defined only for the acute angles. Therefore, students will be introduced with the trigonometry tables for acute angles as a part of their syllabus.Trigonometric table values are normally given for some basic angles such as thiry degrees, forty five degrees, sixty degrees and 90 degrees, etc., And the value for remaining angles can be found using unit circle. Here, trigonometric values can be represented with the help of algebraic expressions. Those are sometimes useful for simplifying solutions into the form of radicals. And these can be further simplified using some basic identities.