What is the exact value of #sec (2pi/3) #? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Nghi N. · mason m May 8, 2015 #sec ((2pi)/3) = 1/cos ((2pi)/3)# On the trig unit circle: #cos ((2pi)/3) = cos (pi - pi/3) = - cos( pi/3) = -1/2# (trig table) #sec ((2pi)/3) = -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 56440 views around the world You can reuse this answer Creative Commons License