mac1147_lecture28_1_c

mac1147_lecture28_1_c - L28 Trigonometric Equations 1...

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342 L28 Trigonometric Equations Example : Solve the equation: 1 sin 2 θ= 1. We compose the inverse function to both sides to find the solution that lies in the Interval of Definition (the principal solution 1 θ ): () 11 1 sin sin sin 2 −− = 1 1 1 sin 26 π == 2. Another solution that lies within the same period with the principal is 2 5 66 =− = 3. All solutions can be obtained by adding an integer number of periods to the solutions above: 2 6 n =+ ( 0, 1, 2,. .. n = ±± ) 5 2 6 n ( .. n = )
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343 Example : Solve the equation: cos a θ= ( 11 a ≤≤ ) 1. We compose the inverse function to both sides to find the solution that lies in the Interval of Definition (the principal solution 1 θ ): cos (cos ) cos a −− = 1 1 cos a = 2. If a −< < , there is another solution that lies within the same period with the principal: 1 2 2c o s a π =− 3. All solutions can be obtained by adding an integer number of periods to the solutions above: 1 cos 2 an =+ 1 (2 cos ) 2 ππ = −+ ( 0, 1, 2,.
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This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture28_1_c - L28 Trigonometric Equations 1...

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