Why does sec(pi/4)= sqrt2? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Nghi N. · Nghi N Sep 23, 2015 Why does #sec (pi/4) = sqrt2# Explanation: #sec ((pi)/4) = 1/(cos (pi/4))# Trig Table of Special arcs gives --> #cos (pi/4) = sqrt2/2.# Therefor #sec (pi/4) = 2/sqrt2 = sqrt2# 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 42501 views around the world You can reuse this answer Creative Commons License