How do you simplify #f(theta)=sin3theta-cos3theta# to trigonometric functions of a unit #theta#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Nghi N. Feb 29, 2016 #f(t) = 3(sin t - cos t)+ 4(cos^3 t - sin^3 t)# Explanation: Use the trig identities: #sin 3t = 3sin t - 4sin^3 t# #cos 3t = 4cos^3 t - 3cos t# #f(t) = sin 3t - cos 3t = 3(sin t - cos t) + 4(cos^3 t - sin^3 t)# 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 2960 views around the world You can reuse this answer Creative Commons License