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Unformatted text preview: 3.7 SOLVING TRIG EQUATIONS Recommended Homework: 3.7: 717, 1927, 3040, 41 52 Trig Equation Worksheet (online) 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, 2) make a table. Example: cos x = 0 G.S.: ______________________________________ In [0, 2) __________________________________ Example: 2cos x + 1 = 0 G.S.: ______________________________________ In [0, 2) __________________________________ Example: sin x cos x + cos x = 0 Solving Trig equations page 1 G.S.: ______________________________________ In [0, 2) __________________________________ Example: tanx = 1 G.S.: ______________________________________ In [0, 2) __________________________________ Example: 2 sin 2 = x Solving Trig equations page 2 G.S.: ______________________________________ In [0, 2) __________________________________ Example: sec x = 2 G.S.: ______________________________________ In [0, 2) __________________________________ Solving Trig equations page 3 Example: 3 tan = 2 x G.S.: ______________________________________ In [0, 2) __________________________________ Solving Trig equations page 4 Example: 1 2 sin 4 = x G.S.: ______________________________________ In [0, 2) __________________________________ Solving Trig equations page 5 Example: sin(3x) 1 = 0 G.S.: ______________________________________ In [0, 2) __________________________________ Solving Trig equations page 6 Example: a) Find all solutions of 3 ) 3 cos( 2 = + x b) Find all solutions in [0, 2 ) of 3 ) 3 cos( 2 = + x Solving Trig equations page 7 Approximating solutions using a calculator. Solve each of the following algebraically in [0, 2) give your answer accurate to 4 decimal places....
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 Fall '10
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 Factoring, Equations

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