Question

Find an exact value. cos 15 please help

Answer 1

Well you want to use a trig identity. Does one come to mind?

Answer 2

1 over sec u?

Answer 3

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?

Answer 4

is there a way to tell which to use?

Answer 5

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:
\[\sqrt{\frac{1 + \cos(30)}{2}} = \sqrt{\frac{1 + \frac{\sqrt3}{2}}{2}}=\frac{\sqrt{2+\sqrt{3}}}{2}\]

Answer 6

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.

Answer 7

Well if the angle is 15 degrees what does that tell you about the sign of cosine? Think of the unit circle.

Answer 8

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?

Answer 9

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.

Answer 10

so then would it be A?

Answer 11

I suppose it would have to be since its the only positive one.