What does sec 2pi equal? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Alan P. Aug 12, 2015 #sec(2pi)=1# Explanation: #sec(theta) = 1/cos(theta)# #color(white)("XXXXXXXX")#(provided #cos(theta)!= 0#) #cos(2pi) = 1# #color(white)("XXXX")##rArr##color(white)("XXXX")##sec(2pi) = 1/1 = 1# 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 12916 views around the world You can reuse this answer Creative Commons License