This is a long comment; hence, community wiki status.
Gamification is not the embedding of educational content into a game. Gamification is the construction of elements typically found in games around a traditional paradigm, whether it be education, training, marketing, etc. This mistaken understanding is a common fallacy and a big reason why there are so many failed attempts at "making learning fun."
Believe it or not, games aren't fun because they're interactive, or have good graphics, or involve knocking things over or shooting things, or anything else like that.
Games are fun because they happen to satisfied a user's intrinsic psychological needs. In fact, most gamers will encounter exceptional frustration at their favorite games. This is certainly not the description of "fun" that most people have!
What games do is they create a framework in which self-actualization is possible. Games synthesize a progression structure in which a user is able to demonstrate competence. Good games also allow a user to dictate their own courses of action, giving them autonomy. And great games allow us to be social with them, creating a sense of relatedness.
Consider any great student: aren't they proud of themselves when they solve a hard problem, even if it frustrated them for hours? Aren't they the ones that like to read three chapters ahead and stay with you after class? Aren't they the ones that like to show their peers the "tricks" they've discovered?
This is what games do. Any mathematical area can be gamified if you do it right. Doing it right is exceptionally hard, which is why most math games are exceptionally boring.
Does adding a colorful graphic make a cosine more fun? No. Does spinning a graph with a mouse make learning about graph theory more fun? No.
None of these things are fun and interesting unless the user is already motivated to see where it goes. To most students, they don't care, so a video game is just a different flavor of worksheet.
If you want to gamify math, don't make the game math. Make the game something else. Make it a story. Give them something to care about, and make mathematics the gateway. Gate rewards behind problems. Scale rewards based on difficulty. The game should have almost nothing to do with mathematics, but rather should motivate students to use the mathematics to uncover the things they're intrigued about.
The star pupil is motivated by learning, and that's great. But the average student doesn't have this motivation, so we need to give it to them somehow. And if you're really clever, you can then tie that story into math, but don't feel like it has to be math. Make it feel like the student can achieve their own goals. Make them want to solve difficult problems and overcome frustration.
If the student hates math, the solution isn't to make the reward more math.
The cosine function takes radians as its argument in most computational languages.
Indeed, $\cos 45^{\circ} = \sqrt{0.5}$, and $\cos 90^{\circ} = 0$. However, in math, for various reasons, we don't like working with degrees. We work with radians, where $2\pi\ \textrm{radians} = 360^{\circ}$.
In fact, $\cos 90\ \textrm{radians} \approx -0.44807$ and $\cos 45\ \textrm{radians} \approx 0.525$.
90 radians would be about 5156 degrees, or about 14.3 turns around the circle!
Best Answer
Notice that the intersections are solutions of
$$\cos(2x)=\pm\cos(x),$$
hence
$$2x=\pm x+2k\pi$$ or $$2x=\pm x+(2k+1)\pi.$$
Finally,
$$x=\frac{k\pi}3.$$
The rest is a matter of sign discussion.