Proper usage of trig functions in force problems

[Matt Armstrong]

Not a particular problem to wonder about but more of a general question, when one has a free body diagram, when is it best to use sine and when is it best to use cosine?

I am reviewing some of my tests for a final, and having previously re-read my forces chapter, I thought that angles rising from the x-axis used sine and angles 'rising' from the y-axis used cosine. However, I have found multiple exceptions to both of these conceptions.

So when is it best to use one or the other?

 

[Doc Al]

As you've discovered, it varies. If a vector F makes an angle θ with some axis, then the component of that vector along the axis (parallel to it) is found using Fcosθ; the component perpendicular to the axis is found using Fsinθ.

But the best thing is to solve a number of problems and practice.

 

[haruspex]

A check I often use is the extreme value test. E.g. if the slope were zero, would my expression for the force give the right result.

 

[CWatters]

It's not "best" to use one of the other. One is usually correct and the other incorrect. Revise the definition of sine and cosine, for example...

Cos(X) = adjacent/hypothenuse

And how to rearrange these equations to give expressions like...

Adj = hyp * Cos(X)

In short you have to get good at looking at drawings and identifying the right angled triangle so you can work out if you need to calculate the adjacent side or the opposite side and if Sin or Cos is needed.

I also use the trick Haruspex mentions.