document.write( "Question 1121000: Solve the system: \"system%28r%2Asin%28theta%29=3%2C+r=4%281%2Bsin%28theta%29%29%29\" \n" ); document.write( "
Algebra.Com's Answer #736732 by Edwin McCravy(20067)\"\" \"About 
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document.write( "Solve the system: \"system%28r%2Asin%28theta%29=3%2C+r=4%281%2Bsin%28theta%29%5E%22%22%29%29\"\r\n" );
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document.write( "Substitute the value of r from the second equation in the first equation:\r\n" );
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document.write( "\"r%2Asin%28theta%29=3\"\r\n" );
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document.write( "\"4%281%2Bsin%28theta%29%5E%22%22%29%2Asin%28theta%29=3\"\r\n" );
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document.write( "\"4%2Asin%28theta%29%2A%281%2Bsin%28theta%29%5E%22%22%29=3\"\r\n" );
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document.write( "\"4%2Asin%5E%22%22%28theta%29%2B4sin%5E2%28theta%29%5E%22%22=3\"\r\n" );
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document.write( "\"4%2Asin%5E%22%22%28theta%29%2B4sin%5E2%28theta%29%5E%22%22-3=0\"\r\n" );
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document.write( "Swap the first two terms:\r\n" );
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document.write( "\"4sin%5E2%28theta%29%5E%22%22%2B4%2Asin%5E%22%22%28theta%29-3=0\"\r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "\"%282sin%28theta%29%2B3%5E%22%22%29%282sin%28theta%29-1%5E%22%22%29=0\"\r\n" );
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document.write( "\"2sin%28theta%29%2B3=0\",   \"2sin%28theta%29-1=0\"\r\n" );
document.write( "\"2sin%28theta%29=-3\",   \"2sin%28theta%29=1\"  \r\n" );
document.write( "\"cross%28sin%28theta%29=-3%2F2%29\",   \"sin%28theta%29=1%2F2\"\r\n" );
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document.write( "All sines are between -1 and +1 so -3/2 is not a possibility,\r\n" );
document.write( "so we ignore the left equation.\r\n" );
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document.write( "\"sin%28theta%29=1%2F2\"\r\n" );
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document.write( "\"theta=matrix%281%2C3%2C30%5Eo%2B360%5Eo%2An%2Cor%2C150%5Eo%2B360%5Eo%2An%29\", if θ is in degrees. \r\n" );
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document.write( "or\r\n" );
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document.write( "\"theta=matrix%281%2C3%2Cpi%2F6%2B2pi%2An%2Cor%2C5pi%2F6%2B2pi%2An%29\", if θ is in radians. \r\n" );
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document.write( "Substituting in the first given equation:\r\n" );
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document.write( "\"r%2Asin%28theta%29=3\"\r\n" );
document.write( "\"r%2A%281%2F2%29=3\"\r\n" );
document.write( "\"expr%281%2F2%29r=3\"\r\n" );
document.write( "\"r=6\"\r\n" );
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document.write( "Edwin
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