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ss_6_6 - Section 6.6 Trigonometric Equations Example Solve...

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Section 6.6 Trigonometric Equations Example. Solve sin θ = 1 2 . Solution. We must find all θ such that sin θ = 1 2 . Note that sin θ = 1 2 when θ = π 6 and θ = 5 π 6 . Hence sin θ = 1 2 if θ = π 6 ± 2 or if θ = 5 π 6 ± 2 for n =0 , 1 , 2 , ··· . –1 –0.5 0.5 1 –1 1 3 579 y =s in θ and y = 1 2 . Example. Solve sin θ = 1 2 for 0 θ< 2 π . Solution. This example is the same as the previous example except that we must choose θ such that θ is in the interval [0,2 π ). From the previous example, θ satisfies the equation sin θ = 1 2 iff θ = π 6 ± 2 or if θ = 5 π 6 ± 2 . The only values of θ in this list that are in the interval [0,2 π ) are θ = π 6 and θ = 5 π 6 . Example. Solve cos2 θ = - 1. Solution. cos α = - 1i f α = π ± 2 . Hence, cos2 θ = - 1i f2 θ = π ± 2 .Th u s , θ = π 2 ± for n =0 , 1 , 2
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ss_6_6 - Section 6.6 Trigonometric Equations Example Solve...

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