How do you find sec of pi/4?

Question

This is a unit circle problem and please include the steps to solve it in the answer.

Answer 1

First recognize that the angle is in radians and also a common triangle (pi/4-pi/4-pi/2 radians or 45-45-90 degrees) will help you to find the exact solution.

The sides of this triangle are as follows: opposite - 1, adjacent - 1, hypotenuse - sqrt(2)

The ratio for secant is the hypotenuse over adjacent (the reciprocal of cosine) = sqrt(2)/1 or simply sqrt(2) 

 

Note: sqrt() stands for square root of what is in parenthesis

Answer 2

sec=1/cos

pi/4=180/4=45º

cos(45º) or cos(pi/4) is equal to √2/2

therefore sec=1/cos=1/(√2/2)=2/√2

now rationalize the denominator

2/√2=2√2/√2√2=2√2/2=√2