My course

Hi there! The video and the problem seen on channels are different versions. Each version marked the correct answer correctly. I will match the version.

Additionally, the video missed the zero point. We should use factorization to get the zero point: $x^2\left(5x^2-3\right)=0$

We solve for all roots as $x^2=0$ and $5x^2-3=0$ .

Hi there! Everything is good, you omitted 'sin' in the denominator.

sin (a) / sin (b) is not the same as sin(a / b).

Hi there! Coordinate systems are arbitrary - They can be rotated to any direction.

We rotate coordinate system to make math easy - If we decompose unknowns like normal force, it will be chaos.

So we decompose known forces such as mg.

I am simply saying that Inclines use a coordinate system parallel/perpendicular to incline surface, not horizontal/vertical. The weight makes an angle to the tilted coordinate system, that's why we decompose weight to mg_y and mg_x.