How is it that sec(pi/4)=sqrt(2) when sec(pi/4)=1/cos(pi/4)=1/sqrt(2)/2=2/sqrt(2)?

Question

The x-coordinate or cosine for 45º or π/4 on a unit circle is sqrt(2)/2.

Answer 1

Because sqrt(2) and 2/sqrt(2) are the same.  You can see this by rationalizing the denominator of 2/sqrt(2) to get  

 

[2/sqrt(2)]*[sqrt(2)/sqrt(2)] = 2*sqrt(2)/2 = sqrt(2)