How do you evaluate #sin ((25pi)/6)#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Eddie Jun 21, 2016 #1/2# Explanation: notice that #(25 pi) / 6 = ((24 + 1) pi) / 6 = 4 pi + pi /6# so you're just looking at #pi/6#. you can ignore the 2 full cycles of #2 pi# #sin (pi / 6) = 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 15931 views around the world You can reuse this answer Creative Commons License