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TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using.

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Presentation on theme: "TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using."— Presentation transcript:

1 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

2 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

3 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

4 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Substituted y = 1

5 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

6 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - simplified

7 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

8 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

9 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. ** since trigonometry is a cyclical function, we must define our answer further.

10 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

11 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

12 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

13 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. ** we will only have to do this when the interval is not already defined

14 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

15 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

16 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Substituted y = 1

17 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Divided both sides by 2

18 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - simplified

19 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

20 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. ** no interval was given

21 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

22 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

23 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - factored

24 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Set each factor = 0 and solve

25 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Set each factor = 0 and solve

26 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Take inverse cos of each side…

27 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Take inverse cos of each side…

28 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

29 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Where does cos x = 1 ???

30 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Where does cos x = 1 ???

31 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

32 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

33 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Added 3 to both sides

34 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - divided both sides by 4

35 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - simplified

36 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Square root of both sides

37 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - simplified

38 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc. - Inverse of both sides

39 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

40 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

41 TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.


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