document.write( "Question 1113736: If csc(α) = 3, where 0 < α <π /2, and β is a Quadrant II angle with tan(β) = −7, find
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Algebra.Com's Answer #728831 by ikleyn(52863)\"\" \"About 
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document.write( "1.  If csc(a) = 3 and the angle \"a\" is in QI, it implies that\r\n" );
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document.write( "    sin(a) = \"1%2F3\"  and  cos(a) = \"sqrt%281-sin%5E2%28a%29%29\" = \"sqrt%281+-+%281%2F3%29%5E2%29\" = \"sqrt%281-1%2F9%29\" = \"sqrt%288%2F9%29\" = \"%282%2Asqrt%282%29%29%2F3\".\r\n" );
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document.write( "2.  If tan(b) = -7  and the angle \"b\" is in QII, it implies that\r\n" );
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document.write( "    cos^2(b) = \"1%2F%281%2Btan%5E2%28b%29%29\" = \"1%2F%281%2B%28-7%29%5E2%29\" = \"1%2F50\"  and  cos(b) = -\"sqrt%281%2F50%29\" = \"-sqrt%2850%29%2F50\" = \"-%285%2Asqrt%282%29%29%2F50\" = \"-sqrt%282%29%2F10\".\r\n" );
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document.write( "    Notice that cos(b) is negative, since \"b\" is in QII.\r\n" );
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document.write( "    Next, knowing cos(b), you can calculate\r\n" );
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document.write( "    sin(b) = \"sqrt%281-cos%5E2%28b%29%29\" = \"sqrt%281-2%2F100%29\" = \"sqrt%2898%2F100%29\" = \"%287%2Asqrt%282%29%29%2F10\".\r\n" );
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document.write( "Answer.  sin(a) = \"1%2F3\".  cos(a) = \"%282%2Asqrt%282%29%29%2F3\".  sin(b) = \"%287%2Asqrt%282%29%29%2F10\".  cos(b) = \"-sqrt%282%29%2F10\".\r\n" );
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