Algebra.Com's Answer #852425 by ikleyn(52968)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Find the angle(s) that would make each statement true.
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document.write( "theta equals arc csc (sqrt of 2)
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document.write( " The solution in the post by @Theo, giving two different possible measures 45 degrees or 135 degrees \r
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document.write( " for the angle  is incorrect.\r
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document.write( " I came to bring a correct solution.\r
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document.write( " =  means, by the definition\r\n" );
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document.write( "  =  and  <= <=  .\r\n" );
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document.write( "For this standard definition, see, for example, this Wikipedia article\r\n" );
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document.write( "https://en.wikipedia.org/wiki/Inverse_trigonometric_functions\r\n" );
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document.write( "In turn, is cosecant \r\n" );
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document.write( " =  .\r\n" );
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document.write( "So, the problem wants you find angle such that\r\n" );
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document.write( " = and <= <= .\r\n" );
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document.write( "In other words, you want to find angle such that\r\n" );
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document.write( "  =  =  and <= <= .\r\n" );
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document.write( "There is only one such angle, and this angle is the standard  of angles, \r\n" );
document.write( "which students learn in Trigonometry course. Its measure is \r\n" );
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document.write( " =  in radians, or = 45 degrees.\r\n" );
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document.write( "ANSWER. The angle satisfying the problem's condition is radians, or 45 degrees.\r\n" );
document.write( " Such an angle is  .\r\n" );
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document.write( "Solved.\r
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document.write( "Perhaps, tens, and hundreds, and thousands students failed to answer this simple question on exam.\r
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document.write( "To answer correctly, it is extremely important to know firmly the definitions .\r
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