Sketch the graphs of each of the following for $x$ in [0,2$\pi$]. list the $x$-axis intercepts of each graph for this interval.
$y=\sqrt{2} \cos \left(x-\frac{\pi}{4}\right)+1$ I tried to solve the equation $y = 0$ by performing the following steps: $\begin{align*} -1&=\sqrt{2} \cos\left(x-\frac{\pi}{4}\right) \\\\ -\frac{1}{\sqrt{2}}&=\cos\left(x-\frac{\pi}{4}\right) \\\\ -\frac{1}{\sqrt{2}}+\frac{\pi}{4}&=\cos(x) \end{align*}$
I'm unable to proceed further. Can you please explain this to me in a step-by-step fashion? And I think that after you've got the answer you have to look the unit circle to get the exact answer. Please also show me how to look for the answer from unit cirle.
Thanks so much!