How do you find the value of #sin2theta# given #costheta=1/3# and #0<theta<90#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Rhys May 19, 2018 # = (4sqrt(2) ) / 9 # Explanation: #sin^2 theta + cos^2 theta = 1 # #=> sin theta = sqrt(1 - cos^2 theta ) # #=> sin theta = (2sqrt(2) ) / 3 # #sin 2 theta = 2 sin theta cos theta # # = 2 * 1/3 * ( 2sqrt(2) ) / 3 # # = (4sqrt(2) ) / 9 # 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 8504 views around the world You can reuse this answer Creative Commons License