#1**+1 **

cos(x)=1/sqrt2 in the intervall pi/12 and 7pi

Hello Guest !

\(cos(x)=\frac{1}{\sqrt{2}}\)

In a square with sides a and the diagonal \(d=a\times \sqrt{2}\)

is the cos of the angle between a and d

\(cos(x)=\frac{a}{d}=\frac{a}{a\times \sqrt{2}}=\frac{1}{\sqrt{2}}\)

This angle is known as 45 °.

So is

\(cos(45°)=\frac{1}{\sqrt{2}}\)

x = 45 °

\(cos(x)=\frac{1}{\sqrt{2}}\)

\(x=arccos(\frac{1}{\sqrt{2}})\\ \color{blue}x\ |\ period\ 2 \pi|\in\{\frac{1}{4}\pi\ ;\ 1\frac{3}{4}\pi\}\)

\(\large\mathbb{L}^{7\pi}_{\frac{\pi}{12}}=\{\frac{1}{4}\pi\ ;\ 2\frac{1}{4}\pi\ ;\ 4\frac{1}{4}\pi\ ;\ 6\frac{1}{4}\pi\ ;\ 1\frac{3}{4}\pi\ ;\ 3\frac{3}{4}\pi\ ;\ 5\frac{3}{4}\pi\}\)

!

asinus Sep 25, 2017