Question

determine the value of sec (-pi/6) without a calculator?

Answer 1

Ok. Here it goes:

\[\sec \theta = 1/\cos \theta\] therefore, let us first find \[\cos (-30) \] which we know is equal to \[\frac{ \sqrt{3} }{ 2}\]. Now, we just invert this and get \[\frac{ 2 }{ \sqrt{3}}\] (the simplifying of this expression is up to you)

note: If you didn't already know, -pi/6 = -30 degrees