pre-calc 5.5

# pre-calc 5.5 - Section 5.5 Trigonometric Equations A...

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Section 5.5 Trigonometric Equations A trigonometric equation is an equation that contains a trigonometric expression with a variable, such as sin x. In this section, we look at trigonometric equations that are true for only some values of the variable. The values that satisfy such an equation are its solutions . example: 2 1 sin = x The period of sine is 2π. All solutions in the interval [0, 2π) are 6 5 , 6 π π = = x x All solutions of 2 1 sin = x are π π π π n x n x 2 6 5 , 2 6 + = + = where n is an integer. Note: There are trigonometric equations that have no solution. EX 1: Use substitution to determine whether the given x-value is a solution of the equation. a) 2 1 cos - = x 3 4 π = x b) 2 2 sin = x 3 π = x c) 3 tan = x 3 π = x Equations Involving a Single Trigonometric Function 1.) Isolate the function on one side of the equation. 2.) Solve for the variable.

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EX 2: Solve the equation 3 sin 3 sin 5 + = x x Equations Involving Multiple Angles EX 3: Solve the equation π 2 0 3 2 tan < = x x EX 4: Solve the equation on the interval [0, 2π) 2 2
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