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Find sin x/2, cos x/2, and tan x/2
\n" ); document.write( "from the given information.
\n" ); document.write( "sec x = 10/9 ,270° < x < 360°
\n" ); document.write( "sin x/2=
\n" ); document.write( "cos x/2=
\n" ); document.write( "tan x/2=
\n" ); document.write( "**
\n" ); document.write( "sec x=10/9=hypotenuse/adjacent side
\n" ); document.write( "hypotenuse=10
\n" ); document.write( "adjacent side=9
\n" ); document.write( "opposite side=√(10^2-9^2)=√(100-81)=√19
\n" ); document.write( "sin x=-√19/10 (in quadrant IV where sin<0)
\n" ); document.write( "cos x=9/10
\n" ); document.write( "..
\n" ); document.write( "Identities:
\n" ); document.write( "sin x/2=±√[(1-cos x)/2]
\n" ); document.write( "choose positive root because x/2 is in quadrant II where sin>0
\n" ); document.write( "sin x/2=√[(1-cos x)/2]=√[(1-9/10/2]=√.1/2=√.05
\n" ); document.write( "..
\n" ); document.write( "cos x/2=±√[(1+cos x)/2]
\n" ); document.write( "choose negative root because x/2 is in quadrant II where cos<0
\n" ); document.write( "cos x/2=-√[(1+cos x)/2]=-√[(1+9/10/2]=-√1.9/2=-√.95
\n" ); document.write( "..
\n" ); document.write( "tan x/2=sin x/(1+cos x)=-(√19/10)/(1+9/10)=-(√19/10)/1.9
\n" ); document.write( "..
\n" ); document.write( "How to check answers with calculator:
\n" ); document.write( "sec x=10/9
\n" ); document.write( "cos x=9/10
\n" ); document.write( "cos^-1=(9/10)≈25.84º (reference angle in specified quadrant IV)
\n" ); document.write( "standard position of angle=360-25.84=334.16
\n" ); document.write( "x/2=334.16/2=167.08
\n" ); document.write( "reference angle=180-167.08=12.92º
\n" ); document.write( "..
\n" ); document.write( "sin x/2=sin 12.92≈0.2236..(in quadrant II where sin>0)
\n" ); document.write( "√.05=0.2236..
\n" ); document.write( "..
\n" ); document.write( "you can check cos x/2 and tan x/2 in the same way \n" ); document.write( "