Question

Find the exact value by using a half-angle identity.
cos(-pi/8)

Answer 1

\[\cos (-\frac{ \pi }{ 8 })\]

Answer 2

Do you know a formula for the half-angle?

Answer 3

I don't have it written down with my others...

Answer 4

Maybe you are familiar with: \(\cos(2\theta)=2\cos^{2}(\theta)-1 \)

Answer 5

\(\bf {\color{blue}{ \cfrac{1}{8}\cdot 2\implies \cfrac{1}{4}}}
\\ \quad \\ \quad \\

cos\left(-\frac{\pi}{8}\right)\implies cos\left(\cfrac{{\color{blue}{ \frac{-\pi}{4}}}}{2}\right)=\pm\sqrt{\cfrac{1+cos\left({\color{blue}{ \frac{\pi}{4}}}\right)}{2}}\)

Answer 6

hmm \(\bf {\color{blue}{ \cfrac{1}{8}\cdot 2\implies \cfrac{1}{4}}}
\\ \quad \\ \quad \\

cos\left(-\frac{\pi}{8}\right)\implies cos\left(\cfrac{{\color{blue}{ \frac{-\pi}{4}}}}{2}\right)=\pm\sqrt{\cfrac{1+cos\left({-\color{blue}{ \frac{\pi}{4}}}\right)}{2}}\)

Answer 7

or \(\bf {\color{blue}{ \cfrac{1}{8}\cdot 2\implies \cfrac{1}{4}}}
\\ \quad \\ \quad \\

cos\left(-\frac{\pi}{8}\right)\implies cos\left(\cfrac{{\color{blue}{ \frac{-\pi}{4}}}}{2}\right)=\pm\sqrt{\cfrac{1+cos\left({\color{blue}{ \frac{-\pi}{4}}}\right)}{2}}\)

anyhow, that's a well known angle that'd be in your Unit Circle

Answer 8

None of my choices look like that.. :(
\[A) \frac{ 1 }{ 2 } \sqrt{2-\sqrt{2}}\]
\[B) \frac{ 1 }{ 2 } \sqrt{1-\sqrt{2}}\]
\[C) \frac{ 1 }{ 2 } \sqrt{2 + \sqrt{2}}\]
\[D) \frac{ 1 }{ 2 } \sqrt{1+\sqrt{2}}\]

Answer 9

you are suppose to simplify what joe what

Answer 10

Do what?

Answer 11

@jdoe0001

Answer 12

I mean wrote

Answer 13

you are suppose to simplify what he wrote

Answer 14

what is cos(-pi/4)
used the fact that it is on the unit circle to find the what cos(-pi/4) is

Answer 15

\( \bf {\color{blue}{ \cfrac{1}{8}\cdot 2\implies \cfrac{1}{4}}}
\\ \quad \\ \quad \\

cos\left(-\frac{\pi}{8}\right)\implies cos\left(\cfrac{{\color{blue}{ \frac{-\pi}{4}}}}{2}\right)=\pm\sqrt{\cfrac{1+cos\left({\color{blue}{ \frac{-\pi}{4}}}\right)}{2}}
\\ \quad \\
\textit{so what's the }cos\left({\color{blue}{ \frac{-\pi}{4}}}\right)\quad ?\)

Answer 16

-sqrt2/2?

Answer 17

So it's positive?

Answer 18

anyhow, yes, but is a POSITIVE amount, since in the IV Quadrant the cosine is positive, thus \(\bf cos\left(-\frac{\pi}{8}\right)\implies cos\left(\cfrac{{\color{blue}{ \frac{-\pi}{4}}}}{2}\right)=\pm\sqrt{\cfrac{1+cos\left({\color{blue}{ \frac{-\pi}{4}}}\right)}{2}}
\\ \quad \\
\implies cos\left(\cfrac{{\color{blue}{ \frac{-\pi}{4}}}}{2}\right)=\pm\sqrt{\cfrac{1+\frac{\sqrt{2}}{2}}{2}}\)

Answer 19

then just simplify the rational

Answer 20

What does that mean?

Answer 21

h..... does . what mean? simplify?

Answer 22

Teachers don't normally allow compound fractions in answers. When we say simplify one of the things you need to make sure of is that there are no compound fractions in your answer.

Answer 23

right, make it a simple fraction inside the radical

Answer 24

I don't get how the 1/2 gets to the outside...