# Trigonometric Equation

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Trigonometric Equation

an algebraic equation involving trigonometric functions of the variables. To solve a trigonometric equation by using different relations among trigonometric functions, the trigonometric equation is converted to a form such that the values of one of the trigonometric functions of the desired variable can be determined. The roots of the trigonometric equation are then found by means of inverse trigonometric functions. For example, sin *x* + sin *2x* + sin *3x* = 0 can be reduced to the form 2 sin *2x* cos *x* + sin *2x* = 0 or sin *2x* (2 cos *x* + 1) = 0; thus, sin *2x* = 0 or cos *x* = – 1/2. This result gives the solutions of the trigonometric equation

where *n* is an arbitrary positive or negative integer.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.