Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

Chapter 15 Trigonometric Identities, Equations and Applications

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 15.4 Trigonometric Equations

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall A trigonometric equation is an equation that contains a trigonometric expression with a variable, such as sin x. To solve an equation containing a single trigonometric function: Isolate the function on one side of the equation. Solve for the variable.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Solve the equation: 3 sin x – 2 = 5 sin x – 1. Solution 1. Isolate the function on one side of the equation. 2. Solve for the variable. We must solve for x in sin x =  1/2. continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Solve the equation: 3 sin x – 2 = 5 sin x – 1. Because Because the period of the sine function is 2 , the solutions of the equations are given by where n is any integer.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Solve the equation: tan 3x = 1, Solution The period of the tangent function is . In the interval [0,  ), the only value for which the tangent function is 1 is  /4. In the interval we obtain the solutions of tan 3x = 1 as follows: (see next slide) continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall These are the solutions to the equation.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Solve the equation: Solution Attempt to solve the equation by factoring.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Solve the equation: Solution Move all the terms to one side. This equation has no solution because sin x cannot be greater than 1 or less than  1.