Why does sec(pi/4)= sqrt2? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Nghi N. ยท 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 43118 views around the world You can reuse this answer Creative Commons License