document.write( "Question 1203483: Hi, can you please help me with this question
\n" ); document.write( "Find the range of x in the interval [0, 2π) for which 8 sin x + cos x > 4.
\n" ); document.write( "The answers are apparently 2arctan(0.2) and 2 arctan(3). I need help with my explanation. Thank you in advance. \n" ); document.write( "

Algebra.Com's Answer #839113 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "In your words

\"Find the range of x in the interval [0, 2π) for which 8 sin x + cos x > 4.\"

I think the word \"range\" should be \"domain\". Anyway:\r\n" );
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document.write( "Then since ,  or \r\n" );
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document.write( "The terms on the left are trig expressions. To make the term 4 on \r\n" );
document.write( "the right become a trig expression also, we play the clever trick \r\n" );
document.write( "of multiplying the 4 by 1, then replacing the 1 by the familiar\r\n" );
document.write( "Pythagorean trig identity :\r\n" );
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document.write( "We use the formulas for sine and cosine of 2y:\r\n" );
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document.write( "One of those factors is positive and the other is negative. So either\r\n" );
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document.write( " or \r\n" );
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document.write( "Those would involve only tan(y) if we divided through by cos(y). We could \r\n" );
document.write( "do that as long as cos(y) is not 0.  Let's make sure cos(y) is not zero.\r\n" );
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document.write( "If cos(y) were 0, then  so let's substitute  in\r\n" );
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document.write( "<--false!\r\n" );
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document.write( "So cos(y) can't be 0. Therefore, we can divide by it. For the first case\r\n" );
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document.write( "Since tangent is a strictly increasing function,\r\n" );
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document.write( "Now since ,\r\n" );
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document.write( "That's the interval you were looking for.  If we considered the other case\r\n" );
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document.write( "it would lead to\r\n" );
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document.write( "which is a contradiction, so the domain is\r\n" );
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document.write( "Edwin

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