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# Hprec8 1

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• Mode &amp; period
• Ex 5, p528
• ### Hprec8 1

1. 1. 8.1: Graphical Solutions to Trigonometric Equations © 2008 Roy L. Gover(www.mrgover.com) Learning Goals: •Solve trig equations graphically. •State the complete solution of a trig equation
2. 2. Example Find the approximate solutions to the following equation using the intersection method: 2 3 3 5 2x x x x− − = − −
3. 3. Example Find the approximate solutions to the following equation using the x intercept method: 2 3 4 3 6x x x x− − = + −
4. 4. Important Idea Many of the methods and ideas we learned about algebraic equations also work with trigonometric equations.
5. 5. Example 1 cos 2 x = Solve by graphing: 1 cosy x=2. Graph 3. Graph 2 1 2 y = 4. Find window 5. Use 2nd Calc 5 to find 2 solutions 6. Use Period to find all solutions 1. Set mode to rads using intersect ion method
6. 6. Important Ideaand always have 2 positive or 2 negative values between 0 and sin x cosx 2π . Find the 1st 2 solutions after 0 with your calculator. 2π
7. 7. Try This tan 2x = 1.1071x kπ= + Solve by graphing: 2
8. 8. Important Idea will have only 1 solution between 0 and tan x (its period). Find the 1st solution after 0; all other solutions are repeats. π 0 π
9. 9. Example Solve sin .85x = − 1. Set mode to rads 2. Re-write 3. Graph 1 sin .85y x= + 4. Find window 5. Find 2 solutions using 2nd calc 2 6. Use period to find all solutions using the x- intercept method
10. 10. Try This Solve using the x intercept method: cos .75x = − 2.419 2x kπ= + 3.864 2x kπ= + and
11. 11. Example Solve 2 3sin cos 2 0x x− − = using the x intercept method. Hint: find all solutions within the period and add 2 kπ to each.
12. 12. Important Idea 1. Write in form ( ) 0f x = 2. Determine period, p 3. Graph over interval p 4. Graphically, find all solutions in interval p 5. Add to solutionkp To solve any trig equation:
13. 13. Example Solve tan 3sin2x x=
14. 14. Try This Solve tan 4cos2x x= − 0.6830 0.9763 1.2801 x k x k x k π π π = − + = + = + 3 non- repeating solutions
15. 15. Important Idea Some real-world applications require that we solve trig equations in degrees instead of radians.
16. 16. Try This What two things are done differently if we solve in degrees instead of radians?
17. 17. Example Solve in degrees: 2 2sin 3sin 3 0θ θ− − =
18. 18. Lesson Close In a future lesson, we will learn to solve trigonometric equations algebraically.