Question 916477
hat is the exact value of sin2x, cos2x and tan2x if tanx=1/2,pi<x<3pi/2
***
hypotenuse of working right triangle=&#8730;(1^2+2^2)=&#8730;5
sinx=1/&#8730;5
cosx=2/&#8730;5
..
sin2x=2sinxcosx=2*1/&#8730;5*2/&#8730;5=4/5
cos2x=cos^2x-sin^2x=4/5-1/5=3/5
tan2x=sin2x/cos2x=4/3
check:
tanx=1/2
x=26.565&#730;
2x=53.13&#730;
..
sin2x=sin53.13&#8776;0.7999...
exact value=4/5=0.8000
..
cos2x=cos53.13&#8776;0.6000
exact value=3/5=0.6000
..
tan2x=tan53.13&#8776;1.3333...
exact value=4/3&#8776;1.3333...