If sintheta=sqrt403/22 and pi/2<theta<pi, how do you find tan2theta? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Hubert Nov 20, 2016 tan2theta=(9sqrt403)/161 Explanation: If theta in [pi/2,pi], costheta<0, so: costheta=-sqrt{1-sin^2theta} costheta=-sqrt{1-403/484}=-sqrt{81/484}=-9/22 tantheta=sintheta/costheta=(sqrt{403}/22)/(-9/22)=-sqrt403/9 tan2theta=(2tantheta)/(1-tan^2theta)=(-(2sqrt403)/9)/(1-403/81)=(-(2sqrt403)/9)/(-322/81)=(9sqrt403)/161 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 2147 views around the world You can reuse this answer Creative Commons License