How do you find the exact value of sin(arctan(2))? Trigonometry Inverse Trigonometric Functions Inverse Trigonometric Properties 1 Answer Chandra S. Sep 7, 2015 Let #alpha# = arctan(2), then, we require the value of sin#alpha# . now tan #alpha# = 2# =># sin#alpha# = 2/#sqrt#5. Explanation: tan#alpha# = 2 #=># y= 2a, x = 2a & r = #sqrt# (5#a^2# ) = #sqrt5# a sin#alpha# = 2a/ #sqrt5# a = 2/#sqrt5# Answer link Related questions How do you use the properties of inverse trigonometric functions to evaluate #tan(arcsin (0.31))#? What is #\sin ( sin^{-1} frac{sqrt{2}}{2})#? How do you find the exact value of #\cos(tan^{-1}sqrt{3})#? How do you evaluate #\sec^{-1} \sqrt{2} #? How do you find #cos( cot^{-1} sqrt{3} )# without a calculator? How do you rewrite #sec^2 (tan^{-1} x)# in terms of x? How do you use the inverse trigonometric properties to rewrite expressions in terms of x? How do you calculate #sin^-1(0.1)#? How do you solve the inverse trig function #cos^-1 (-sqrt2/2)#? How do you solve the inverse trig function #sin(sin^-1 (1/3))#? See all questions in Inverse Trigonometric Properties Impact of this question 11457 views around the world You can reuse this answer Creative Commons License