Algebra.Com's Answer #651112 by ikleyn(52797)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Evaluate the expression under the given conditions\r
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document.write( "sin(θ − ϕ); tan θ = 12/5, θ in Quadrant III, sin ϕ = -(sqrt 10)/10 , ϕ in Quadrant IV
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document.write( "To evaluate  you will use the formula \r\n" );
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document.write( " =  . (1)\r\n" );
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document.write( "To use this formula, you need to know  ,  ,  and  .\r\n" );
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document.write( "Is it given to you? - Only in part: you are given \" =  and  is in Q4\".\r\n" );
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document.write( "Regarding  , you are given that \" =  and is in Q3\".\r\n" );
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document.write( "So, your first task is, based on the given data, find , and .\r\n" );
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document.write( "You have =  =  =  =  =  .\r\n" );
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document.write( " The sign \"-\" was chosen for the square root, because the sine is negative for an angle in Q3.\r\n" );
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document.write( "Having = , you can easily calculate \r\n" );
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document.write( " =  =  =  =  =  =  .\r\n" );
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document.write( " The sign \"-\" was chosen for the square root, because the cosine is negative for an angle in Q3.\r\n" );
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document.write( "Next, =  =  =  =  =  .\r\n" );
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document.write( " The sign \"+\" was chosen for the square root, because the cosine is positive for an angle in Q4.\r\n" );
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document.write( "Let us summarize what we have so far: = , = , = and = .\r\n" );
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document.write( "Now you can plug-in this data into the formula (1) and get\r\n" );
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document.write( " =  =  =  =  . \r\n" );
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document.write( "Answer. = .\r\n" );
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document.write( "For many other similar problems see the lessons \r
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document.write( " - Calculating trigonometric functions of angles\r
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document.write( " - Advanced problems on calculating trigonometric functions of angles\r
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document.write( "in this site.\r
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