document.write( "Question 960664: determine if it is possible for a number t to satisfy the given conditions sint=5/13 and cost=12/13 \n" ); document.write( "

Algebra.Com's Answer #854564 by ikleyn(53875) $\"\"$ $\"About$

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\n" ); document.write( "determine if it is possible for a number t to satisfy the given conditions sin(t) = 5/13 and cos(t) = 12/13.
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\n" ); document.write( "\n" ); document.write( "This problem assumes totally different solution from that in the post by @lwsshar3.\r
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document.write( "The only thing which you should to check is this equality\r\n" );
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document.write( "    sin^2(t) + cos^2(t) = 1    (1)\r\n" );
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document.write( "for given values sin(t) and cos(t).\r\n" );
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document.write( "So, we calculate\r\n" );
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document.write( "     +  =  +  =  =  = 1.\r\n" );
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document.write( "We see that equality (1) is held. It means that such an angle 't' (in radians) does exist \r\n" );
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document.write( "    t = arcsin(5/13) = arccos(12/13).\r\n" );
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document.write( "Actually, 't' is the measure of an angle arctan(5/12).\r\n" );
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document.write( "So, the answer to the problem's question is \"Yes\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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