What is the exact value for cos(pi/12)? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer José F. Apr 27, 2016 #sqrt(2+sqrt(3))/2# Explanation: #color(blue)(cos(x/2)=+-sqrt((1+cos(x))/2))# We know that #cos(pi/6)=sqrt(3)/2#. So, #cos(pi/12)=sqrt((1+sqrt(3)/2)/2)=sqrt((2+sqrt(3))/4)=sqrt(2+sqrt(3))/2# http://www.purplemath.com/modules/idents.htm 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 2849 views around the world You can reuse this answer Creative Commons License