Question

cos(-7pi/12)
Using half-angle I get:
Sqrt((2-sqrt3)/4)
Is this correct?
What is the sign?

Answer 1

So you would be using -7pi/6, which is the same as 5pi/6 in the positive direction. Either way, I just like positive angles:

\[\sqrt{\frac{ 1+\cos \frac{ 5 \pi }{ 6 } }{ 2 }}= \sqrt{\frac{ 1-\frac{ \sqrt{3} }{ 2 } }{ 2 }}\]
\[\sqrt{\frac{ \frac{ 2-\sqrt{3} }{ 2 } }{ 2 }}= \sqrt{\frac{ 2-\sqrt{3} }{ 4 }}= \frac{ 1 }{ 2 }*\sqrt{2-\sqrt{3}}\]
Look slike you did fine, you can just factor the 4 denominator out of the root.

Answer 2

why isn't it negative?

Answer 3

The negative is inside of there. Theres nowhere else a negative could be really. No matter value of cosine any trig function you pick, youre going to have any negative sign inside of the root.

Answer 4

i mean why isn't it
-(1/2)sqrt(2-sqrt3)
since cosine of -7pi/12 is negative

Answer 5

Youre right, I just left out the +/- in front of the formula as I was typing it.

Answer 6

I never put it in and only did the square root portion.

Answer 7

hey thanks for the help! so its both +/- or only -?

Answer 8

Well, the formula should just naturally have a +/- in front of it. Then which one you select is knowledge of the quadrant youre in.

Answer 9

k thanks