document.write( "Question 86882: please solve this problem: please solve the trigonometric equation\r
\n" ); document.write( "\n" ); document.write( " $\"+cos%282x%29\"$ - $\"sIn%5E2x%2F2+\"$ + $\"3%2F4\"$ = $\"0\"$ \r
\n" ); document.write( "\n" ); document.write( "give all positive values of the angle between 0 to 360 degress give any approximate value to the nearest minute only. \n" ); document.write( "

Algebra.Com's Answer #63032 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "please solve this problem: please solve the trigonometric equation \r\n" );
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document.write( " -  +  =  \r\n" );
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document.write( "give all positive values of the angle between 0 to 360 degress \r\n" );
document.write( "give any approximate value to the nearest minute only. \r\n" );
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document.write( " -  +  = \r\n" );
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document.write( "Multiply the equation through by LCD = 4\r\n" );
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document.write( " -  +  =  \r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( " -  +  = \r\n" );
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document.write( "Use the identity cos 2q = 1 - 2sin²q\r\n" );
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document.write( "to substitute 1 - 2sin²x for cos(2x) in the first term:\r\n" );
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document.write( " -  +  = \r\n" );
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document.write( "Remove the parentheses by distributing:\r\n" );
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document.write( " -  +  = \r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( "Take the square roots of both sides:\r\n" );
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document.write( " = ±\r\n" );
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document.write( " = ±\r\n" );
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document.write( "Find the inverse sine of .836600265 in the\r\n" );
document.write( "first quadrant:\r\n" );
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document.write( " = 56.78908924°\r\n" );
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document.write( "To change the decimal part of that to minutes, \r\n" );
document.write( "multiply the decimal part .78908924 by 60, getting\r\n" );
document.write( "47.34535435' then round to the nearest minute, so\r\n" );
document.write( "the value of x is the first quadrant is 56°47'.\r\n" );
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document.write( "But since the  can be positive or \r\n" );
document.write( "negative, we will get all the angles in all the\r\n" );
document.write( "quadrants which have 56²47 as their reference\r\n" );
document.write( "angles.\r\n" );
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document.write( "The second quadrant answer is found by\r\n" );
document.write( "subtracting 56°47' from 180° or\r\n" );
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document.write( "180° - 56°47' = 179°60' - 56°47' = 123°13'\r\n" );
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document.write( "The third quadrant answer is found by\r\n" );
document.write( "adding 56°47' to 180° or\r\n" );
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document.write( "180° + 56°47' = 236°47'\r\n" );
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document.write( "The fourth quadrant answer is found by\r\n" );
document.write( "subtracting 56°47' from 360°\r\n" );
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document.write( "360° - 56°47' = 359°60' - 56°47' = 303°13'\r\n" );
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document.write( "So all the answers for x between 0° and 360° are\r\n" );
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document.write( "x = 56°47', 123°13', 236°47', and 303°13\r\n" );
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document.write( "Edwin

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