anonymous
  • anonymous
Find an exact value. cos 15 please help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Well you want to use a trig identity. Does one come to mind?
anonymous
  • anonymous
1 over sec u?
anonymous
  • anonymous
Well we need a numerical value and the only values we know 'closed form' or 'exact' answers for are a select few. Some of these include, 30, 45, 90, 180, etc. So what would you want to use then?

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anonymous
  • anonymous
is there a way to tell which to use?
anonymous
  • anonymous
Not a very common formula but the one I believe you need is given by: \[\cos \left( \frac{\theta}{2} \right) = \sqrt{\frac{1 + \cos(\theta)}{2}}\] In this case: \[\frac{\theta}{2} = 15 \implies \theta = 30^o\] So just plug that in: \[\sqrt{\frac{1 + \cos(30)}{2}} = \sqrt{\frac{1 + \frac{\sqrt3}{2}}{2}}=\frac{\sqrt{2+\sqrt{3}}}{2}\]
anonymous
  • anonymous
sorry im really stupid xD plug that long thing into my calculator? because these are my choices quantity square root of six plus square root of two divided by four. quantity negative square root of two plus square root of six divided by four. quantity negative square root of six minus square root of two divided by four. quantity negative square root of six plus one divided by four.
anonymous
  • anonymous
Well if the angle is 15 degrees what does that tell you about the sign of cosine? Think of the unit circle.
anonymous
  • anonymous
I have a unit circle right in front of me and I know which quadrants have the trig functions that are positive and I see the degrees but I don't see 15 degrees?
anonymous
  • anonymous
Well 15 degrees is between what, 0 and 30 right? Which means the cosine of that, which corresponds to the x component, is positive. However, in the form I have given it, none of the answer choices match. This means we must use another formula I would assume.
anonymous
  • anonymous
so then would it be A?
anonymous
  • anonymous
I suppose it would have to be since its the only positive one. |dw:1378506737998:dw|
anonymous
  • anonymous
that's what I was thinking so i have a bunch of ones like that just continue to look at the unit circle like for ex i have an other one like cos 165 degrees

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