Int. J. Appl. Comput. Math (2019) 5:44 https://doi.org/10.1007/s40819-019-0600-8 ORIGINAL PAPER A New Trigonometrical Algorithm for Computing Real Root of Non-linear Transcendental Equations Vivek Kumar Srivastav 2 · Srinivasarao Thota 1 · Manoj Kumar 3 © Springer Nature India Private Limited 2019 Abstract This paper presents a new algorithm to find a non-zero real root of the transcendental equa- tions using trigonometrical formula. Indeed, the new proposed algorithm is based on the combination of inverse of sine series and Newton Raphson method, which produces better approximate root than Newton Raphson method. The implementation of the proposed algo- rithm in MATLAB is also discussed. Certain numerical examples are presented to show the efficiency of the proposed algorithm. This algorithm will help to implement in the commercial package for finding a real root of a given transcendental equation. Keywords Algebraic equations · Transcendental equations · Newton Raphson method · Sine inverse function Mathematics Subject Classification 65Hxx · 65H04 Introduction There are several methods available in literature for finding a root of transcendental equations. The main objective of existing algorithms is to provide higher order guaranteed convergence. In literature, there are many well known numerical methods (Bisection, Secant, Regula- Falsi, Newton-Raphson, Muller’s methods etc.) to calculate an approximate root of algebraic or transcendental equations. The present proposed algorithm is based on trigonometrical B Vivek Kumar Srivastav vivekapril@gmail.com Srinivasarao Thota srinithota@ymail.com Manoj Kumar manoj@mnnit.ac.in 1 Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Post Box No. 1888, Adama, Ethiopia 2 Department of Mathematics and Computing, Motihari College of Engineering, Motihari, India 3 Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, India 0123456789().: V,-vol 123