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TrigEquations-1 - 3.7 SOLVING TRIG EQUATIONS Recommended...

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3.7 SOLVING TRIG EQUATIONS Recommended Homework: 3.7: 7-17, 19-27, 30-40, 41- 52 Trig Equation Worksheet (on-line) Strategies for solving trig equations algebraically: Apply basic algebra techniques such as factoring, squaring etc. to isolate the trig function. If necessary, try applying trig identities. Our goal is to get trig (something) = # Use the unit circle or reference angles to find the principal angles If you want all solutions, add k* fundamental period Solve for your variable If you need a solution in an interval such as [0, 2π) make a table. Example: cos x = 0 G.S.: ______________________________________ In [0, 2π) __________________________________ Example: 2cos x + 1 = 0 G.S.: ______________________________________ In [0, 2π) __________________________________ Example: sin x cos x + cos x = 0 Solving Trig equations page 1
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G.S.: ______________________________________ In [0, 2π) __________________________________ Example: tanx = -1 G.S.: ______________________________________ In [0, 2π) __________________________________ Example: 2 sin 2 = x Solving Trig equations page 2
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G.S.: ______________________________________ In [0, 2π) __________________________________ Example: sec x = 2 G.S.: ______________________________________ In [0, 2π) __________________________________ Solving Trig equations page 3
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Example: 0 3 tan = - 2 x G.S.: ______________________________________ In [0, 2π) __________________________________ Solving Trig equations page 4
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Example: 0 1 2 sin 4 = - x G.S.: ______________________________________ In [0, 2π) __________________________________ Solving Trig equations page 5
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Example: sin(3x) – 1 = 0 G.S.: ______________________________________ In [0, 2π) __________________________________ Solving Trig equations page 6
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Example: a) Find all solutions of 0 3 ) 3 cos( 2 = - + π x b) Find all solutions in [0, 2 π ) of 0 3 ) 3 cos( 2 = - + π x Solving Trig equations page 7
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Approximating solutions using a calculator. Solve each of the following algebraically in [0, 2π) give your answer accurate to 4 decimal places. Example: 3 cos x – 2 = 0 Example: 5 cos x + 1 = 0 Solving Trig equations page 8
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Example: 3 sin x + 2 = 0 Example: 2 csc x - 5 = 0 Solving Trig equations page 9
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NOTE: When you are approximating a solution on your calculator, you must ALWAYS - Identify the quadrants of your answer - Find the reference angle - Show ALL reference angle work exactly BEFORE plugging to calculator.
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