document.write( "Question 1062077: How do I solve the equation Find all solutions to Tan(theta-30 degrees)= -5 Book answers 131.3 and 311.3. I am not able to solve the equation and get the results of the correct answers. \n" ); document.write( "
Algebra.Com's Answer #676857 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "\"+tan%28theta+-+30%29+=+-5+\"
\n" ); document.write( "\"++theta+-+30+=+arctan%28-5%29+\"
\n" ); document.write( "\"+++theta+=+arctan%28-5%29+%2B+30+\"
\n" ); document.write( "\"++theta+=+-78.69+%2B+30+\"
\n" ); document.write( "\"+theta+=+-48.69+degrees+\" <<< ordinarily, this is acceptable b/c arctan(x) is by default expressed
\n" ); document.write( " as an angle between -90 and +90 degrees. \r
\n" ); document.write( "\n" ); document.write( "Now, \"all solutions\" adds a bit more work. We need to look to see where tan(x) is positive and where it is negative.
\n" ); document.write( "—
\n" ); document.write( "Recall tan(x) = sin(x)/cos(x)
\n" ); document.write( "--
\n" ); document.write( "Q1: sin(x) is +, cos(x) is + —> tan(x) is +
\n" ); document.write( "Q2: sin(x) is +, cos(x) is - —> tan(x) is -
\n" ); document.write( "Q3: sin(x) is -, cos(x) is - —> tan(x) is +
\n" ); document.write( "Q4: sin(x) is -, cos(x) is + —> tan(x) is -
\n" ); document.write( "—
\n" ); document.write( "Therefore, all of the angles (0…360 degrees) that satisfy theta=-48.69 = arctan(x) are:
\n" ); document.write( " #1: -48.69 + 360 = 311.31 degrees (in Q4)
\n" ); document.write( " #2: -48.69 + 180 = 131.31 degrees (in Q2)\r
\n" ); document.write( "\n" ); document.write( "—\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "#1: tan (311.31-30) = tan(281.31) = -5
\n" ); document.write( "#2: tan(131.31-30) = tan(101.31) = -5
\n" ); document.write( "—\r
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );