5.3 SOLVING TRIGONOMETRIC EQUATIONS（5.3解三角方程）.pdfVIP

5.3 SOLVING TRIGONOMETRIC EQUATIONS Copyright © Cengage Learning. All rights reserved. What You Should Learn • Use standard algebraic techniques to solve trigonometric equations. • Solve trigonometric equations of quadratic type. • Solve trigonometric equations involving multiple angles. • Use inverse trigonometric functions to solve trigonometric equations. 2 Introduction 3 Introduction To solve a trigonometric equation, use standard algebraic techniques such as collecting like terms and factoring. Your preliminary goal in solving a trigonometric equation is to isolate the trigonometric function in the equation. For example, to solve the equation 2 sin x = 1, divide each side by 2 to obtain 4 Introduction To solve for x, note in Figure 5.6 that the equation has solutions x = /6 and x = 5/6 in the interval [0, 2). Figure 5.6 5 Introduction Moreover, because sin x has a period of 2, there are infinitely many other solutions, which can be written as and General solution where n is an integer, as shown in Figure 5.6. 6 Introduction Another way to show that the equation has infinitely many solutions is indicated in Figure 5.7. Any angles that are coterminal with /6 or 5/6 will also be solutions of the equation. When solving trigonometric equations, you should write your answer(s) using exact values rather than decimal approximations.