Trigonometric Equations OBJECTIVES: Use standard algebraic techniques to solve trigonometric equations Solve trigonometric equations of quadratic type.

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Presentation transcript:

Trigonometric Equations OBJECTIVES: Use standard algebraic techniques to solve trigonometric equations Solve trigonometric equations of quadratic type

Introduction O To solve a trigonometric equation, use standard algebraic techniques (when possible) such as collecting like terms and factoring. Your preliminary goal in solving a trigonometric equation is to isolate the trigonometric function on one side of the equation.

Solve the trigonometric equation O To solve the equation for x O These solutions are in the interval But there are infinitely many other solutions

EX 1: Solve O A)

EX 1: Solve O B)

EX 1: Solve O C)

EX 1: Solve O D)

Solving Equation O The equations in Example 1 involved only one trigonometric function. When two or more functions occur in the same equation, collect all terms on one side and try to separate the functions by factoring, using the Quadratic Formula or by using appropriate identities. This may produce factors that yield no solutions.

EX 2: Solve O A)

EX 2: Solve O B)

EX 2: Solve O C)

Solving Equations O Sometimes you must square each side of an equation to obtain a quadratic. Because this procedure can introduce extraneous solutions, you should check any solutions in the original equation to see whether they are valid or extraneous.

EX 3: Solve O A)

EX 2: Solve O B)