14 April Kidoguchi, Kenneth
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1 Objectives.. Solve Trigonometric Equations Using a Calculator. 3. Solve Trigonometric Equations Quadratic in Form. 4. Solve Trigonometric Equations Using Fundamental Identities. 5. Solve Trigonometric Equations Using a Grahing Utility. 14 Aril Kidoguchi, Kenneth
2 Determine whether q = /4 is a solution of the equation: sin q 0 Is q = 5/4 a solution? 14 Aril 018 Kidoguchi, Kenneth
3 Let: f 6.3 Trigonometric Equations Determine whether q = /4 is a solution of the equation: sin q 0 Is q = 5/4 a solution? f q q sin / 4 sin / 4 0 f 5 / 4 sin 5 / Aril Kidoguchi, Kenneth
4 Solve the equation: cos q 3 0 Give a general formula for all solutions. List eight of the solutions. 14 Aril Kidoguchi, Kenneth
5 Solve the equation: cos q 3 0 Give a general formula for all solutions. List eight of the solutions. q 6 1 k1 14 Aril Kidoguchi, Kenneth
6 Solve the equation: cos q 3 0 Give a general formula for all solutions. List eight of the solutions. cosq 3 0 cosq 3 3 cosq k 6 q k 6 q k 6 1 k1 6, k 14 Aril Kidoguchi, Kenneth
7 Solve the equation: cos q 3 0 Give a general formula for all solutions. List eight of the solutions ,,, q Aril Kidoguchi, Kenneth
8 Solve the equation: sin q 0, 0 q 14 Aril Kidoguchi, Kenneth
9 Solve the equation: sin q 0, 0 q 14 Aril Kidoguchi, Kenneth
10 Solve the equation: sin q 0, 0 q sin q k 4 q, k k 4 k 4 q 3 k 4 k 8 q 3 k 8 14 Aril Kidoguchi, Kenneth
11 Solve the equation: k 8 q 3 k k8 3 k8 sin q 0, 0 q 14 Aril Kidoguchi, Kenneth
12 Solve the equation: 3 tan 3q 1 0, 0 q 14 Aril Kidoguchi, Kenneth
13 Solve the equation: 1 tan 3q 3 3 q n, n 6 n q n 18 3 tan 3q 1 0, 0 q 14 Aril Kidoguchi, Kenneth
14 Solve the equation: q n 3 tan 3q 1 0, 0 q n q /18 5/18 11/18 17/18 3/18 9/18 35/18 41/18 14 Aril Kidoguchi, Kenneth
15 q q 4 Solve the equation: cos 1, 0 14 Aril Kidoguchi, Kenneth
16 q q 4 q 0 k, k ^ 0 q 4 q k 4 1k8 4 4 Solve the equation: cos 1, 0 14 Aril Kidoguchi, Kenneth
17 . Solve Trigonometric Equations Using a Calculator. Use a calculator to solve the equation: cos(q) =0., 0 < q <. Exress any solutions in radians, rounded to two decimal laces. 14 Aril Kidoguchi, Kenneth
18 3. Solve Trigonometric Equations Quadratic in Form. Solve the equation: cos (q) cos(q) 1 = 0, 0 < q <. 14 Aril Kidoguchi, Kenneth
19 3. Solve Trigonometric Equations Quadratic in Form. Solve the equation: cos (q) cos(q) 1 = 0, 0 < q <. x 0 cos cos 1 Let cos q q q x x 1 x 1 x 1 Which requires: 1 cosq 1 0 cosq cos q 1 0 cos q 1 14 Aril Kidoguchi, Kenneth
20 4. Solve Trigonometric Equations Using Fundamental Identities Solve the equation: sin (q) sin(q) = cos (q), 0 < q <. q q q 1 sin q q q x q sin sin cos sin sin 1 0 Let sin x x 1 x 1 x 1 Which requires: sin q 1 0 sin q sin q 1 0 sin q Aril Kidoguchi, Kenneth
21 4. Solve Trigonometric Equations Using Fundamental Identities Solve the equation: sin (q) + cos(q) = 3, 0 < q <. in q 1 cos q t x cos 03 s cos q 3 cos q cos q cos q Le q x 1 1 x x N.B.: 0 sin q 1 and 1 cos q 1 14 Aril Kidoguchi, Kenneth
22 5. Solve Trigonometric Equations Using a Grahing Utility Solve the equation: 3cos(x) + x = 4, 0 < q <. Exress the solution(s) rounded to two decimal laces. 14 Aril 018 Kidoguchi, Kenneth
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