Question

If cos (A) = 1/2 with A in QIV, find sec (A/2).

Answer 1

Cos(A) = 1/2 means A = 60 degrees. But, since it is in fourth quadrant, it means A = 270+60 degrees = 330 degrees.

So, A/2 = 330/2 = 165
So, sec(A/2) = sec(165) = -1.035

Answer 2

or, if you want the exact value use the half-angle formula for cosine and take the reciprocal...

Answer 3

So, what would be the exact angle? I'm sorry, I'm just confusing myself.

Answer 4

no, I mean the exact value for sec(165 degrees)...

Answer 5

that is, if the exact value is required...

Answer 6

Right... So, how would I write the equation? I only have three kinds I learned about, and they are sin, cos, and tan. I don't know how to find sec from cos, though I know they are opposite reciprocals.
And, yes. We do have to have the exact value.

Answer 7

sec = 1/cos

Answer 8

ok. so you're familiar with the half-angle formula?

Answer 9

secant is reciprocal of cosine.

Answer 10

In the above, I calculated cos(165) and did its inverse to figure out sec(165).

Answer 11

Yes, dpalnc. I just don't know how to use it very well.

Answer 12

here's the half-angle formula for cosine: