document.write( "Question 814143: sin (θ + 4°) = cos (θ + 6°) \n" ); document.write( "
Algebra.Com's Answer #490341 by Edwin McCravy(20056)\"\" \"About 
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document.write( "sin(θ + 4°) = cos(θ + 6°)\r\n" );
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document.write( "Use the cofunction identity  cos(a) = sin{90°-a)\r\n" );
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document.write( "sin(θ + 4°) = sin[90° - (θ + 6°)]\r\n" );
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document.write( "sin(θ + 4°) = sin[90° - θ - 6°)]\r\n" );
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document.write( "sin(θ + 4°) = sin(84° - θ)\r\n" );
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document.write( "Then we use the fact that\r\n" );
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document.write( "if sin(α) = sin(β)\r\n" );
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document.write( "then one or both of these\r\n" );
document.write( "hold\r\n" );
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document.write( "α = β + 360°n\r\n" );
document.write( "α = (180°-β) + 360°n\r\n" );
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document.write( "for integer n\r\n" );
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document.write( "Using the first one\r\n" );
document.write( "     α = β + 360°n\r\n" );
document.write( "θ + 4° = 84° - θ + 360°n\r\n" );
document.write( "    2θ = 80° + 360°n\r\n" );
document.write( "     θ = 40° + 180°n \r\n" );
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document.write( "letting n=0 give θ = 40°\r\n" );
document.write( "letting n=1 give θ = 220°\r\n" );
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document.write( "Using the second one\r\n" );
document.write( "     α = 180° - β + 360°n\r\n" );
document.write( "θ + 4° = 180° - (84 - θ) + 360°n\r\n" );
document.write( "θ + 4° = 180° - 84° + θ + 360°n\r\n" );
document.write( "    4° = 96° + 360°n\r\n" );
document.write( "  -92° = 360°n\r\n" );
document.write( "  \"-92%2F360\" = n\r\n" );
document.write( "   \"-23%2F90\" = n\r\n" );
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document.write( "That is extraneous because n is an integer.\r\n" );
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document.write( "So the only solutions between 0° and 360° are\r\n" );
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document.write( "θ = 40° and θ = 220°\r\n" );
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document.write( "and the general solution is  \r\n" );
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document.write( "θ = 40° + 180°n, for any integer n.\r\n" );
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document.write( "Edwin
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