document.write( "Question 672645: Use the given information to find cos(x/2), sin(x/2), and tan(x/2):
\n" ); document.write( "tan x = 2, pi < x < 3pi/2\r
\n" ); document.write( "\n" ); document.write( "Here is my solution, but I don't know how to get sin(x/2) and tan(x/2):
\n" ); document.write( "1 + (2)^2 = sec^2x
\n" ); document.write( "5 = sec^2x
\n" ); document.write( "sec x = -sqrt(5)
\n" ); document.write( "cos x = -1 / sqrt(5) = -sqrt(5)/5
\n" ); document.write( "cos^2(x/2) = 1/2(1+(-sqrt(5)/5))
\n" ); document.write( " = 5-(sqrt(5)/10)
\n" ); document.write( "cos(x/2) = -sqrt(5-sqrt(5)/10)
\n" ); document.write( "sin^2(x/2) = 1/2(1-(-sqrt(5)/5))
\n" ); document.write( " = 5+(sqrt(5)/10)
\n" ); document.write( "sin(x/2) = ?
\n" ); document.write( "tan(x/2) = ? \n" ); document.write( "
Algebra.Com's Answer #418248 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Use the given information to find exact values of cos(x/2), sin(x/2), and tan(x/2):
\n" ); document.write( "tan x = 2, pi < x < 3pi/2
\n" ); document.write( "**
\n" ); document.write( "Given information shows that x is in quadrant III, where cos<0, sin<0, tan>0
\n" ); document.write( "tanx=2=opp side/adj side=2/1
\n" ); document.write( "hypotenuse=√(2^2+1^2)=√(4+1)=√5
\n" ); document.write( "sinx=opp side/hypotenuse=-2/√5
\n" ); document.write( "cosx=adj side/hypotenuse=-1/√5
\n" ); document.write( "..
\n" ); document.write( "use half-angle identities to solve
\n" ); document.write( "cos(x/2)=±[√(1+(cosx)/2)]
\n" ); document.write( "=-[√(1-(1/√5)/2)]
\n" ); document.write( "=-[√(√5-1)/2√5)]
\n" ); document.write( "..
\n" ); document.write( "sin(x/2)=±[√(1-(cosx)/2)]
\n" ); document.write( "=-[√(1+(1/√5)/2)]
\n" ); document.write( "=-[√(√5+1)/2√5)]
\n" ); document.write( "..
\n" ); document.write( "tan(x/2)=sinx/(1+cosx)
\n" ); document.write( "=-2√5/(1-(1/√5)
\n" ); document.write( "=-2√5/(√5-1)/√5
\n" ); document.write( "=-2/√5-1
\n" ); document.write( " \n" ); document.write( "
\n" );