document.write( "Question 945488: Find the exact value of tangent of theta over 2 given tangent of theta = negative 5 over 8 and theta is between 3 pi over 2 and 2 pi. . \n" ); document.write( "

Algebra.Com's Answer #576679 by lwsshak3(11628) $\"\"$ $\"About$

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Find the exact value of tangent of theta over 2 given tangent of theta = negative 5 over 8 and theta is between 3 pi over 2 and 2 pi.
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\n" ); document.write( "given tanx=-5/8 (3π/2,2π)
\n" ); document.write( " $\"tan%28x%2F2%29=sinx%2F%281%2Bcosx%29\"$
\n" ); document.write( "Hypotenuse of reference right triangle in quadrant IV
\n" ); document.write( "= $\"sqrt%285%5E2%2B8%5E2%29=sqrt%2825%2B64%29=sqrt%2889%29\"$
\n" ); document.write( "sinx=-5/√89=-5√89/89
\n" ); document.write( "cosx=8/√89=8√89/89
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\n" ); document.write( "..
\n" ); document.write( "Check:
\n" ); document.write( "tanx=-5/8 (Q4)
\n" ); document.write( "x≈327.9946˚
\n" ); document.write( "x/2≈162.997˚
\n" ); document.write( "tan(x/2)=tan(162.997≈-0.2868..(from calculator)
\n" ); document.write( "exact value as computed:= $\"%28-5sqrt%2889%29%29%2F%2889%2B8sqrt%2889%29%29\"$ ≈-0.2868..
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