Question #97b1d
1 Answer
Nov 21, 2017
Explanation:
#"using the "color(blue)"half-angle identities"#
#•color(white)(x)sin(x/2)=+-sqrt((1-cosx)/2)#
#•color(white)(x)cos(x/2)=+-sqrt((1+cosx)/2)#
#•color(white)(x)tan(x/2)=+-sqrt((1-cosx)/(1+cosx))#
#"in the third quadrant only the tangent is positive"#
#"all the identities require "cosx#
#•color(white)(x)cosx=+-sqrt(1-sin^2x)#
#rArrcosx=-sqrt(1-(-20/29)^2)=-sqrt(1-400/841)#
#color(white)(rArrcosx)=-sqrt(441/841)=-21/29#
#rArrsin(x/2)=-sqrt(25/29)=-5/sqrt29=-5/29sqrt29#
#rArrcos(x/2)=-sqrt(4/29)=-2/sqrt29=-2/29sqrt29#
#rArrtan(x/2)=sqrt((50/29)/(8/29))=25/4#