How do I find the value of sec 5pi / 6? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Somebody N. Apr 1, 2018 #color(blue)(-(2sqrt(3))/3# Explanation: #sec((5pi)/6)# Identity: #color(red)bb(sec(x)=1/cos(x))# #cos((5pi)/6)=-cos(pi-(5pi)/6)=-cos(pi/6)=-sqrt(3)/2# #sec((5pi)/6)=1/-cos((pi)/6)=1/((-sqrt(3))/2)=color(blue)(-(2sqrt(3))/3# 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 38044 views around the world You can reuse this answer Creative Commons License