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# PRECALC ALG & TRIG MAC 1147

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This 12 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1147 at University of Florida taught by Larissa Williamson in Fall. Since its upload, it has received 16 views. For similar materials see /class/207048/mac-1147-university-of-florida in Calculus and Pre Calculus at University of Florida.

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Date Created: 09/19/15

L22 Trigonometric Equations Example Solve the equation sin6 1 We compose the inverse function to both sides to nd the solution that lies in the Interval of De nition the principal solution 91 sin 1sin 9 sin 1 1 7r 6 sin 1 1 2 6 2 Another solution that lies Within the same period with the principal is 7 57 92 7 7 6 3 All solutions can be obtained by adding an integer number of periods to the solutions above 9 27m n0ili2 V 95 27m n0rlr2 Example Solve the equation cos6a lSaSl 1 We compose the inverse function to both sides to nd the solution that lies in the Interval of De nition the principal solution 61 cos 1cos 6 cos 1 a 61 cos 1 a 2 If 1 lt a lt1 there is another solution that lies Within the same period with the principal 62 27 cos 1 a 3 All solutions can be obtained by adding an integer number of periods to the solutions above 6 cos 1 a 27m 6 27 cos 1 a 27m n0ili2 Example Solve the equation tan6a ooltaltoo 1 We compose the inverse function to both sides to find the principal solution 61 that lies in the Interval of De nition tan 1 tan 6 tan 1 a 61 tan 1 a 2 All solutions can be obtained from the principal by adding an integer number of periods 6tan71a7m n0ili2 316 Solving Trigonometric Eguations 1 Reduce the equation to one of the forms sin6a cos6a lSaSl tan6a cot6 a ooltaltoo 2 Compose the inverse function to both sides to find the solution which lies in the Interval of Definition the principal solution 61 3 Find another solution 62 that lies within the same period with the principal if any 4 Find the desired solutionsall solutions by adding integer number of periods to the ones found in steps 2 and 3 317 Example Find all solutions of the equation List the ones that lie on the interval 0271 sin97l 2 Example List the solutions that are in the interval 0271 Find all solutions of the equation cos9 2 2 K Example Find a general formula for all solutions of the equation List three solutions that are closest to O l tan6 E 320 Example Solve the equation on the interval 027r sin 26 1 3 321 Example Solve the equation cos26sin61 7rlt6 7r 322 Example Find all solutions of the equations cos63 sin6 O3 323 Example Solve the equation cos26 cos6 O O S 6 lt 27 324 Summary and General Formulas for the Solutions E t Principal A1110 All solutions qua to solution so u w n Oi1i2 on the period 1 sm6a 6 Sin1a 627r sm1a 6 sm a27m lt lt 1 1a1 1ltalt1 6 sin1a27m 6 62 27 COS 1 a 6 cos 1 a 27m COS a 61 cos 1 a 1 S a S 1 71 1ltalt1 6227r cos a27rn tan a 6 1 tan 1 a 6 tan 1 a 7m cot a 61 cot 1 a 6 cot 1 a 7m 325

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