document.write( "Question 1201599: Find the exact values of sin 2𝜃, cos 2𝜃, and tan 2𝜃 for the given value of 𝜃.
\n" ); document.write( "cot 𝜃 = 3/4;180° < 𝜃 < 270° \n" ); document.write( "

Algebra.Com's Answer #836058 by ikleyn(52915) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find the exact values of sin 2a, cos 2a, and tan 2a for the given value of a.
\n" ); document.write( "cot(a) = 3/4;180° < a < 270°.
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Since  180° < a < 270°,  angle  \"a\"  is in the 3rd quadrant, QIII.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "From the definition of the cot-function, it is the ratio of the attached leg to the opposite leg.\r\n" );
document.write( "\r\n" );
document.write( "    So, the attached leg to angle \"a\" of the right angled triangle is 3 units long horizontally, opposite to x-axis;\r\n" );
document.write( "        the opposite leg to angle \"a\" of the right angled triangle is 4 units long vertically,   opposite to y-axis.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The hypotenuse is 5 units long  ( 5 =  =  ).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, sin(a) = ;  cos(a) = .  The signs are  \"-\",  because we are in QIII.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore\r\n" );
document.write( "\r\n" );
document.write( "    sin(2a) = 2*sin(a)*cos(a) =  = .\r\n" );
document.write( "\r\n" );
document.write( "    cos(2a) =  =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "By the way, it means that angle \"2a\" is in QII.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next,  tan(2a) =  =  = .\r\n" );
document.write( "

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

\n" );