How do you evaluate #sin((23pi)/6) #? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Sidharth Mar 3, 2016 #sin ((23pi)/6) = -1/2# Explanation: #sin ((23pi)/6)# #= sin (690) = sin (2*360 - 30)= sin (-30) = - sin30# #sin 30 = 1/2# #=>sin 690 = -1/2# 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 9487 views around the world You can reuse this answer Creative Commons License