Application of the Method of Trigonometrical Substitution in Solving Problems

Abstract

The use of trigonometric substitution in solving algebraic problems aims to establish a relationship between different branches of mathematics, namely: algebra and trigonometry. It is important to instill in students courage and resourcefulness in finding ways to solve problems not only in the immediate environment of the conditions, but also in a wider, sometimes unexpected area. Trigonometric substitution is one of many substitution methods of integration where a function or expression in a given integral is replaced by trigonometric functions such as sin, cos, tan, etc. Integration by replacement is a good and easiest approach that anyone can make. It is used when we replace the function, whose derivative is already included in the given integral function. This simplifies the function and gives a function of simple integrals that we can easily integrate. It is also known as u-substitution or reverse chain rule Or in other words, using this method, we can easily evaluate integrals and antiderivatives.