Question #97b1d

1 Answer
Nov 21, 2017

#"see explanation"#

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#