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7.4.2 – Solving Trig Equations, Cont’d • Sometimes, we may have more than one trig function at play while trying to solve • Like having two variables >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 • Example. Solve the equation sin2x + cos2x + tan2x = 0. • Example. Solve the equation cosx – 1 = sinx – Hint: treat the left side as a binomial. 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 • Example. Verify for the equation that x = 2π/3 is a solution to 2 cosx + 1 = 0. 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 • 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 • Example. Estimate the solutions to the equation x tan(x) – 3 = 0 on the interval [0, 2π) • Example. Estimate the solutions to the equation 2 sin x = 1 – 2 cos x on the interval [0, 2π) • Assignment • Pg. 586 • 13, 17, 33, 39, 42, 45