I've been trying to find materials/examples for a problem that goes something like this:
You are given the function f(x)=$\frac{1}{2}$cos x. Solve the equation f(x)=$\frac{1}{\sqrt{8}}$ within range [0;2$\pi$].
My question is, what is this topic, exactly? The above problem has too little documentation in my native language so I tried translating it(poorly) and searching for cosine function/trigonometry but that doesn't seem tight enough. Could someone tell me the related topics or keywords for this problem or maybe even a source with materials, if possible?
This is equivalent to $$\cos x=\sqrt\frac12,$$ which is true for every $$x=\pm\frac{\pi}{4}+2\pi n,\qquad n\in\mathbb Z.$$ Since we are in the range $[0, 2\pi]$, the only solutions are $$x=\frac14\pi\lor x=\frac74\pi.$$
You can also think of $\pi/4$ as an angle. Then, take a rectangular triangle with this angle ($\pi/4=45^\circ$) and lenth $1$ of the hypotenuse. Then, the other two sides have to have length $1/\sqrt2$, which you can prove using Pythagoras theorem. Thus, you have proven the relation (because then, $\cos(\pi/4)=\frac{1/\sqrt2}{1}$ by the geometric definition of cosine).