When should I use cosine or sine for sum of forces in the y or x direction?

[eseefreak]

I attached an image of the problem I am currently working on. I am having a hard time understanding when to use cosine or sine when referring to the sum of the forces in the y direction or x direction. I have a general understanding as to where you initially place your coordinate system. If you take a look at the solution you will see that the sum of the forces in the y direction uses cos25, instead of my initial reaction to use sin25.

If anyone can help with visual examples of different situations that would be amazing. I understand doing that would be a lot of work so any advice is also much appreciated.

Thank you so much!

 

[DrClaude]

One way to quickly check if you made the right choice is to think about the physics, while keeping in mind that, for angles less than 90°, the cosine is bigger for smaller angles, and the reverse is true for the sine.

In the problem you have, think what happens if you reduce the angle of the ramp: the blocks will slide less, and the downward force due to the mass must increase. Therefore, for y you use the cosine of the angle, and sine for x.

 

[eseefreak]

Thank you for the help!