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Published byRaymond Cameron Modified over 9 years ago
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7.4.2 – Solving Trig Equations, Cont’d
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Sometimes, we may have more than one trig function at play while trying to solve Like having two variables
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>1 trig function When we have more than one trig function, we want to try and simplify the equation in terms of a single trig function How? – Use identities – Expand or factor using algebra – Write in terms of sine and cosine, combine – Look for any like terms to cancel
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Example. Solve the equation sin 2 x + cos 2 x + tan 2 x = 0.
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Example. Solve the equation cosx – 1 = sinx – Hint: treat the left side as a binomial.
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Verifying Solutions Similar to algebra, we must be able to verify that solutions of particular equations are accurate Options: – 1) Plug in, pull values from table – 2) Use calculator, be careful of typing answers in
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Example. Verify for the equation that x = 2π/3 is a solution to 2 cosx + 1 = 0.
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Using your calculator Sometimes, finding exact solutions may not be feasible In this event, we will jump to using our calculators, and treating them as an algebraic expression
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To use your calculator: – 1) Write the function with all terms on a single side – 2) Plug in into your “graph” section – 3) Select an appropriate range – 4) Use the “find-zero” feature we have used before
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Example. Estimate the solutions to the equation x tan(x) – 3 = 0 on the interval [0, 2π)
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Example. Estimate the solutions to the equation 2 sin x = 1 – 2 cos x on the interval [0, 2π)
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Assignment Pg. 586 13, 17, 33, 39, 42, 45
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