a. y= 5x 2 +2x 3 d. 2x+5=10 b. y= 3 x 2 c. y= 1 x 3 Learning Goal QUIZ Trigonometric Identities. OH nooooooo! Class Opener: March 17, 2015

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1 DAY 48 March 16/17, 2015 OH nooooooo! Class Opener: Find D and R: a. y= 5x 2 +2x 3 b. y= 3 x 2 c. y= 1 x 3 +2 d. 2x+5=10 Nov 14 2:45 PM Learning Goal QUIZ Trigonometric Identities. Mar 13 11:56 AM 1

] sin 2 (3x) = (sin (3x)) 2 Feb 14 2:54 PM LESSON 5.3. SOLVING TRIGONOMETRIC EQUATIONS 1.] 2sin(y) = sin(2y) 2.] cos 2 (y) = cos(y 2 ) False False 3.

2 IN YOUR NOTES LESSON 5.3. SOLVING TRIGONOMETRIC EQUATIONS Determine whether the following equations are true or false: 1.] 2sin(y) = sin(2y) 2.] cos 2 (y) = cos(y 2 ) 3.] 3tan(x 2 ) 5tan(x 2 ) = 2 tan (x 2 ) 4.] cos(3y) + cos(y) = cos (4y) 5.] cos(y) + cos(x) = cos (x+y) 6.] sin 2 (3x) = (sin (3x)) 2 Feb 14 2:54 PM LESSON 5.3. SOLVING TRIGONOMETRIC EQUATIONS 1.] 2sin(y) = sin(2y) 2.] cos 2 (y) = cos(y 2 ) False False 3.] 3tan(x 2 ) 5tan(x 2 ) = 2 tan (x 2 ) True 4.] cos(3y) + cos(y) = cos (4y) False 5.] cos(y) + cos(x) = cos (x+y) False 6.] sin 2 (3x) = (sin (3x)) 2 True Feb 14 2:54 PM 2

3 Lesson 5.3. Solving Trigonometric Equations (Easy cases) When solving a trigonometric equation, your goal is to isolate the trigonometric function involved in the equation using standard algebraic operations and trigonometric identities. When solving algebraic equations, we can always CHECK (code word for verify) solutions. Example: Verify that each x value is a solution of the equation given: 1.] 2 cos(x) 1 = 0 (a) x = π/3 (b) x = 5π/3 2.] sec x 2 = 0 (a) x = π/3 (b) x = 5π/3 Feb 14 7:51 PM Verifying solutions for Trig Equation: Example: Verify that each x value is a solution of the equation given: Note: solution to the equation is "zero" of the equation 1.] 2 cos(x) 1 = 0 (a) x = π/3 (b) x = 5π/3 2.] sec x 2 = 0 (a) x = π/3 (b) x = 5π/3 Feb 14 10:43 PM 3

4 Lesson 5.3. Solving Trigonometric Equations (Easy cases) When solving a trigonometric equation, your goal is to isolate the trigonometric function involved in the equation using standard algebraic operations and trigonometric identities. When solving algebraic equations, we can always CHECK (code word for verify) solutions. Example 1: Solve 2sinx 1 = 0 for x. Feb 28 3:14 PM Lesson 5.3. Solving Trigonometric Equations (Easy cases) When solving a trigonometric equation, your goal is to isolate the trigonometric function involved in the equation using standard algebraic operations and trigonometric identities. When solving algebraic equations, we can always CHECK (code word for verify) solutions. Example 1: Solve 2sinx 1 = 0 for x. There are an infinite number of solutions to this problem. To solve for x, you must first isolate the sine term. therefore The sine function is positive in quadrants I and II. Therefore, two of the solutions to the problem are and Numerical Check: Left Side: Right Side: 0 Feb 28 3:14 PM 4

5 Solve 2sinx 1 = 0 for x. Therefore, two of the solutions to the problem are and These two solutions are solution on the interval [0, 2π], but there are infitinely many solutions id the domain is not restricted to a specific interval. There will be 2 solution in every 2π revolutions. If you rotate from π/6 exactly 2π radians, you will hit your next solution. If you rotate from 5π/6 exactly 2π radians, you will hit your next solution. Therefore, ALL GENERAL SOLUTIONS WILL BE where n is the number of revolutions in positive/negative direction. Feb 28 3:29 PM Solve for x: General solutions: Feb 16 2:11 PM 5

6 Note: General solutions for tangent repeat every π radians! Feb 16 2:14 PM Feb 16 2:19 PM 6

7 Feb 16 2:28 PM General Solutions: Feb 17 3:26 PM 7

8 Rewriting as a Single Trigonometric Function: Feb 16 8:41 AM Remember to use ± when taking the square root!!! Feb 17 11:11 AM 8

9 Feb 14 10:55 PM Lesson / 2 30 EVEN An Answer Key posted on Mrs. Ghillany's LMSA Web Page Feb 16 9:38 AM 9

SESSION 6 Trig. Equations and Identities. Math 30-1 R 3. (Revisit, Review and Revive)

SESSION 6 Trig. Equations and Identities Math 30-1 R 3 (Revisit, Review and Revive) 1 P a g e 2 P a g e Mathematics 30-1 Learning Outcomes Specific Outcome 5: Solve, algebraically and graphically, first