Reteaching 14.6 Solving Trigonometric Equations

NAME _________________________________________________ CLASS _______________ DATE ______________Reteaching14.6 Solving Trigonometric Equations◆Skill A Solving trigonometric equations algebraically and graphicallyRecallTrigonometric equations are true only for certain values of the variable, unlikeidentities which are true for all values of the variable.Copyright © by Holt, Rinehart and Winston. All rights reserved.◆ Example 1Find all the solutions for each equation algebraically.a. sin 3 sin b. 2 cos 2 5 cos 2 0◆ Solutiona. sin 3 sin b. 2 cos 2 5 cos 2 02 sin 3sin 32 240 n(360)or 300 n(360)where n is any integer◆ Example 2Solve sin x 2 cos x for 0 x 2π graphically.◆ Solution4sin x 2 cos xUse radian mode on your calculator.y 1 sin x and y 2 2 cos xThese two graphs intersect atx 1.11 and x 4.25, whichare the solutions of theoriginal equation.Find all possible solutions for each equation algebraically.1. 2 cos 3 02.3. 2 sin 2 sin 04.(2 cos 1)(cos 2) 02 cos 1 0 60 n(360)or 300 n(360)–42 cos 1cos 1 2tan 3 0ororsin 2 5 sin 6 0cos 2 0cos 2(not possible)Solve each equation for 0 x 2π graphically.5. 2 cos2 x cos x 16.sin x sin 1 2 x7. tan 2 x 1 tan x8. 3 sin 2x cos xAlgebra 2 Reteaching 14.6 185

NAME _________________________________________________ CLASS _______________ DATE ______________◆Skill B Solving trigonometric equations containing more than one trigonometricfunction algebraicallyRecallcsc 1sin tan sin cos sin 2 cos 2 1sec 1cos cot cos sin cot 1tan tan 2 1 sec 2 ◆ ExampleSolve sin 2 x 3 cos x 3 0 for 0 x 2π.◆ Solutionsin 2 x 3 cos x 3 01 cos 2 x 3 cos x 3 0cos 2 x 3 cos x 2 0cos 2 x 3 cos x 2 0(cos x 1)(cos x 2) 0cos x 1 0 or cos x 2 0cos x 1 or cos x 2x 0 or 2π(not possible)1 cot 2 csc 2 Solve each equation for 0 x 2π.9. sin x cot x 110.csc x sin 2 x 1 011. sin 2 x cos x 1 012.2(1 cos 2 x) sin x 113. cos x sin x14. tan x cot x 1Copyright © by Holt, Rinehart and Winston. All rights reserved.186 Reteaching 14.6 Algebra 2