How do you evaluate #sin((2pi)/3)#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Alan P. May 5, 2016 #sin((2pi)/3)=color(green)(sqrt(3)/2)# Explanation: since #sin(theta)# is defined as the #("opposite side")/("hypotenuse")# for an angle #theta# #color(white)("XXX")sin((2pi)/3)=sqrt(3)/2# (as can be seen form the diagram above) Answer link Related questions How do you find the trigonometric functions of any angle? What is the reference angle? How do you use the ordered pairs on a unit circle to evaluate a trigonometric function of any angle? What is the reference angle for #140^\circ#? How do you find the value of #cot 300^@#? What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#? How do you know if #sin 30 = sin 150#? How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle Impact of this question 36162 views around the world You can reuse this answer Creative Commons License