document.write( "Question 1203962: If \"+cos%28beta%29+=+-3+%2F+5+\" then, without a calculator, find \"cos%28pi+%2F+2+-+beta%29+\". Write your answer as a fraction. \n" ); document.write( "
Algebra.Com's Answer #839909 by ikleyn(52890)\"\" \"About 
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\n" ); document.write( "If \"+cos%28beta%29+=+-3+%2F+5+\" then, without a calculator, find \"cos%28pi+%2F+2+-+beta%29+\".
\n" ); document.write( "Write your answer as a fraction.
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document.write( "\"cos%28pi%2F2-beta%29\" = \"cos%28pi%2F2%29%2Acos%28beta%29+%2B+sin%28pi%2F2%29%2Asin%28beta%29\" = \"0%2Acos%28beta%29+%2B+1%2Asin%28beta%29\" = \"sin%28beta%29\" = +/- \"sqrt%281-cos%5E2%28beta%29%29\" = \r\n" );
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document.write( "= +/- \"sqrt%281-%28-3%2F5%29%5E2%29\" = +/- \"sqrt%281-9%2F25%29\" = +/- \"sqrt%2816%2F25%29\" = +/- \"4%2F5\".\r\n" );
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document.write( "Thus, there are two solutions and two answers are possible, 4/5 or -4/5, \r\n" );
document.write( "depending on to which quadrant the angle \"beta\" does belong.\r\n" );
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document.write( "ANSWER.  If \"beta\" is in QII, then  \"cos%28pi%2F2-beta%29\" = 4/5.\r\n" );
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document.write( "         If \"beta\" is in QIII, then  \"cos%28pi%2F2-beta%29\" = -4/5.\r\n" );
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