How do you find the value of #sin(theta/2)# given #costheta=-4/5# and #90<theta<180#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Ratnaker Mehta Jan 26, 2017 #sin(theta/2)=+3/sqrt10.# Explanation: Recall that #cos2x=1-2sin^2x.# #:. cos theta=1-2sin^2(theta/2)# #:. 2sin^2(theta/2)=1-(-4/5)=9/5# #:. sin^2(theta/2)=9/10# #:. sin(theta/2)=+-3/sqrt10# But, #90 lt theta lt 180 rArr 90/2 lt theta/2 lt 180/2, i.e.,# #45 lt theta/2 lt 90," or, "theta/2" lies in the "1^(st)" Quadrant".# #"Therefore, "sin(theta/2)=+3/sqrt10.# Answer link Related questions What are Double Angle Identities? How do you use a double angle identity to find the exact value of each expression? How do you use a double-angle identity to find the exact value of sin 120°? How do you use double angle identities to solve equations? How do you find all solutions for #sin 2x = cos x# for the interval #[0,2pi]#? How do you find all solutions for #4sinthetacostheta=sqrt(3)# for the interval #[0,2pi]#? How do you simplify #cosx(2sinx + cosx)-sin^2x#? If #tan x = 0.3#, then how do you find tan 2x? If #sin x= 5/3#, what is the sin 2x equal to? How do you prove #cos2A = 2cos^2 A - 1#? See all questions in Double Angle Identities Impact of this question 7921 views around the world You can reuse this answer Creative Commons License