anonymous
  • anonymous
If cos (A) = 1/2 with A in QIV, find sec (A/2).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
or, if you want the exact value use the half-angle formula for cosine and take the reciprocal...
anonymous
  • anonymous
So, what would be the exact angle? I'm sorry, I'm just confusing myself.

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anonymous
  • anonymous
no, I mean the exact value for sec(165 degrees)...
anonymous
  • anonymous
that is, if the exact value is required...
anonymous
  • anonymous
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.
anonymous
  • anonymous
sec = 1/cos
anonymous
  • anonymous
ok. so you're familiar with the half-angle formula?
anonymous
  • anonymous
secant is reciprocal of cosine.
anonymous
  • anonymous
In the above, I calculated cos(165) and did its inverse to figure out sec(165).
anonymous
  • anonymous
Yes, dpalnc. I just don't know how to use it very well.
anonymous
  • anonymous
here's the half-angle formula for cosine: |dw:1333572888846:dw|
anonymous
  • anonymous
since we need to find sec(165) = 1/cos(165), then A = 330 degrees. follow me so far?
anonymous
  • anonymous
Sure do!!
anonymous
  • anonymous
now the exact value of cos(330) = srt3/2, correct?
anonymous
  • anonymous
Correct.
anonymous
  • anonymous
so we just plug that in to the formula: |dw:1333573177862:dw|
anonymous
  • anonymous
now, about the +, - which one do we choose?
anonymous
  • anonymous
hint... 165 degrees is in what quadrant? what is the sign of cosine in that quadrant?
anonymous
  • anonymous
QII, so -!!
anonymous
  • anonymous
good... i also simplified what's in the radical... |dw:1333573386151:dw|
anonymous
  • anonymous
\[{\sqrt{2+\sqrt{3}}}/2\] ??? :D
anonymous
  • anonymous
- in front. Sorry. lol
anonymous
  • anonymous
yes... this is cosine of 165 degrees. so if we want secant of 165, just take the reciprocal of that answer...
anonymous
  • anonymous
How come you divide by 4?
anonymous
  • anonymous
|dw:1333573583482:dw|
anonymous
  • anonymous
I see now... So, since you are not allowed to have radicals on the bottom, do I have to multiply to get the reciprocal?
anonymous
  • anonymous
yes..
anonymous
  • anonymous
welll, how does your teacher feel about that?
anonymous
  • anonymous
because in calculus, we're allowed to have radicals in the denominator...
anonymous
  • anonymous
Feel about finding the reciprocal? Yeah, she won't let us have radicals in the denominator.
anonymous
  • anonymous
yeah, that's usually what most teachers say... no radicals in the denominator... in AP calc, we can leave our answers with radicals in the denominator.
anonymous
  • anonymous
Wow... Well, hopefully, I won't have to do this later.
anonymous
  • anonymous
yep. good work man!...
anonymous
  • anonymous
Thanks! I appreciate the help! This online homework... Just, ugh. Lol.

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