document.write( "Question 927047: Tanθ=cot(30°+5θ)
\n" ); document.write( "Use the cofunction identities to find an angle θ that makes the statement true \n" ); document.write( "

Algebra.Com's Answer #562653 by Edwin McCravy(20064) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "tan(θ) = cot(30°+5θ)\r\n" );
document.write( "\r\n" );
document.write( "Since tan(θ) = cot(90°-θ)\r\n" );
document.write( "\r\n" );
document.write( "and you only want one value of θ,\r\n" );
document.write( "\r\n" );
document.write( "Replace tan(θ) by cot(90°-θ)\r\n" );
document.write( "\r\n" );
document.write( "cot(90°-θ) = cot(30°+5θ)\r\n" );
document.write( "\r\n" );
document.write( "     90°-θ = 30°+5θ\r\n" );
document.write( "       60° = 6θ\r\n" );
document.write( "       10° = θ\r\n" );
document.write( "\r\n" );
document.write( "[To get all the solutions, since tangent and cotangent\r\n" );
document.write( "have period 180°, add n*180° to 90°-θ \r\n" );
document.write( "\r\n" );
document.write( "cot(90°-θ+n*180°) = cot(30°+5θ)\r\n" );
document.write( "\r\n" );
document.write( "90°-θ+n*180° = 30°+5θ\r\n" );
document.write( "  60°+n*180° = 6θ\r\n" );
document.write( "   10°+n*30° = θ where n is any integer, positive, negative or zero. \r\n" );
document.write( "The solutions are given by this sequence:\r\n" );
document.write( "\r\n" );
document.write( "..., -140°, -110°, -80°, -50°, -20°, 10°, 40°, 70°, 100°, 130°, 160°,... \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );