document.write( "Question 1076776: If csc (theta) <0 and cos(theta)=5/13, find sin (theta/2) and cos (theta/2). \n" ); document.write( "
Algebra.Com's Answer #691475 by ikleyn(52786)\"\" \"About 
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\n" ); document.write( "If csc (theta) <0 and cos(theta)=5/13, find sin (theta/2) and cos (theta/2).
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document.write( "\"csc%28theta%29\" < \"0\" means \"sin%28theta%29\" < \"0\".\r\n" );
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document.write( "Together with \"cos%28theta%29\" = \"5%2F13\", it means that \"theta\" is the angle in QIV.\r\n" );
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document.write( "Hence,  \"theta%2F2\" is the angle in QII.\r\n" );
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document.write( "Then  \"sin%28theta%2F2%29\" = \"sqrt%28%281-cos%28theta%29%29%2F2%29\" = \"sqrt%28%281-%285%2F13%29%29%2F2%29\" = \"sqrt%28%2813-5%29%2F%2813%2A2%29%29\" = \"sqrt%288%2F26%29\" = \"2%2Fsqrt%2813%29\" = \"%282%2Asqrt%2813%29%29%2F13\".\r\n" );
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document.write( "The sign is \"+\" since sine is positive in QII.\r\n" );
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document.write( "\"cos%28theta%2F2%29\" = \"-sqrt%28%281%2Bcos%28theta%29%29%2F2%29\" = \"-sqrt%28%281%2B%285%2F13%29%29%2F2%29\" = \"-sqrt%28%2813%2B5%29%2F%2813%2A2%29%29\" = \"-sqrt%2818%2F26%29\" = \"-sqrt%289%2F13%29\" = \"%28-3%29%2Fsqrt%2813%29\".\r\n" );
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document.write( "The sign is \"-\" since cosine is negative in QII.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see more solved similar problems on calculating trig functions look into the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on calculating trigonometric functions of angles\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Trigonometry: Solved problems\". \r
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