Find the exact value of the trigonometric function:

Question

sec(-pi/12)

I am not sure how to answer this off the unit circle.

Answer 1

You should know that
sec (-pi/12)
= 1/cos(-pi/12)
= 1/cos(pi/12)

You might find it "easier" to visualize degrees than radians, if so, the
pi/12 radians = 15º

so we need cos 15º

cos15 = cos(45-30) ... (I am dropping the º symbol for easier typing)

= cos45cos30 + sin45sin30
= (√2/2)(√3/2) + (√2/2)(1/2)
= (√6 + √2)/4

and
cos(-pi/12) = 4/(√6 + √2)