Hello,

The equation is as follows:

$\displaystyle \cos 2\left( x_{+\frac{\pi }{8}} \right)=-\left( \frac{1}{\sqrt{2}} \right)$

With the interval $\displaystyle \left[ 0,2\pi \right]$.

So what I did was let $\displaystyle 2x+\frac{\pi }{4}=\frac{3\pi }{4}$ and $\displaystyle 2x+\frac{\pi }{4}=\frac{5\pi }{4}$ since cos is negative in the 2nd and 3rd quadrants with a basic angle of $\displaystyle \frac{\pi}{4}$.

I then continued to solve the two equations and ended up with x=$\displaystyle \frac{\pi }{4}$ and $\displaystyle \frac{\pi }{2}$.

However I'm missing out the two angles $\displaystyle \frac{5\pi }{4}$ and $\displaystyle \frac{3\pi }{2}$. I'm supposed to be adding $\displaystyle 2\pi$ to $\displaystyle \frac{\pi }{4}$ and $\displaystyle \frac{\pi }{2}$ right? But it doesn't give me the other two angles that I missed out.

Also, regarding intervals, when I multiply the a number into the brackets, does it change? Like for the above when I multiply the 2 to get 2x, does the interval get multiplied by two also? That is $\displaystyle \left[ 0,4\pi \right]$.