What is Sec pi/12?

Question

I need help to find the exact value of sec pi/12 and rounding to two decimals places. Please explain

Answer 1

It's the reciprocal of cos (½•pi/6).

 

To obtain an exact answer, use the half angle formula for cosine. 

 

Then you can take the reciprocal of cos 15^o on the calculator.

 

Check your exact answer by converting it to decimal; that and the above result should agree.

Answer 2

Sec(pi/12)=1/cos(pi/12)=1/cos[(1/2)*(pi/6)]=√2/(1+cos(pi/6))=√2/(1+√3/2)=..,=√2(-1+√3)