# Proper usage of trig functions in force problems

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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?

Mentor
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.

• Chestermiller and Matt Armstrong
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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.

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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...