document.write( "Question 488238: sin 2x + cos 60 = 0, 0 < x < 360.
\n" ); document.write( "i have been able to find out that sin inverse of -1/2 is -30, but how do i find answers in the 3rd and fourth quadrant for 2x?? then i can find x. my answers are coming wrong, and i can apply no suitable rule. please help, and show working if possible. \n" ); document.write( "

Algebra.Com's Answer #852359 by ikleyn(52864) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "sin 2x + cos 60 = 0, 0 < x < 360.
\n" ); document.write( "i have been able to find out that sin inverse of -1/2 is -30, but how do i find answers in the 3rd and fourth quadrant
\n" ); document.write( "for 2x?? then i can find x. my answers are coming wrong, and i can apply no suitable rule. please help, and show
\n" ); document.write( "working if possible.
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\n" ); document.write( "\n" ); document.write( "In the post by @Theo, you will not find the answers for x,
\n" ); document.write( "so, the reader is in the dark about how to complete the solution.\r
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\n" ); document.write( "\n" ); document.write( "I came to make the job from the beginning to the end.\r
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document.write( "The starting equation is in degrees\r\n" );
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document.write( "    sin(2x) + cos(60°) = 0.\r\n" );
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document.write( "As you know, cos(60°) = -1/2,  so, you equation becomes\r\n" );
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document.write( "    sin(2x) + 1/2 = 0,  or  sin(2x) = -1/2.\r\n" );
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document.write( "You should know the table angles.  If sin(2x) = -1/2, it means\r\n" );
document.write( "that angle 2x is in 3rd or 4th quadrant\r\n" );
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document.write( "    2x = 210°  or  2x = 330°.\r\n" );
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document.write( "It implies that  x = 210°/2 = 105°  or  x = 330°/3 = 165°.\r\n" );
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document.write( "ANSWER.  The given equation has two solutions,  x = 105°  and/or  x = 165°.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved from the beginning to the end, with complete explanations
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