I’m a senior in high school and I don’t know how to choose sin or cos in physics problem. For the most part I memorised them. For example, why is the flux of a magnetic field = BAcos(angle) and why is the electromagnetic force = ILBsin(angle).
The last two years weren’t normal as we studied online so it’s highly appreciated if someone can eli5 and fill in the gaps for me.
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Sine and Cosine are functions that describe the ratios of the lengths of different sides in a right-angle triangle. If you draw a right-angled triangle, pick one of the other angles, Sine tell you about the ratio of the side opposite that angle to the longest side, Cosine tells you about the ratio of the side next to the angle to the longest side.
So they are really useful when doing anything involving triangles.
What we’re doing in electromagnetism is slightly different, though. The 19th century physicists working on electromagnetism had to invent a whole new area of maths to help understand this area, and unfortunately we tend not to teach it to you in school. So you are trying to solve problems that the people who developed this area needed new maths to solve, but without that maths. Which is why it is a bit confusing and a bit of a fudge.
Anyway… Generally, what is going on when we have sines and cosines is that we have two “things” (vectors) that are pointing in different directions, with some angle between them. Our basic formulae assume that either those things are in the same direction, or are at right-angles (flux = BA, or EM Force = ILB). If they aren’t, we need to add in a scale factor to account for the angle. That is either going to be cosine or sine as these essentially tell us how much of one vector is in the two different directions compared with the second vector (either in the same direction, or in the perpendicular direction); this is why it comes up a lot when resolving forces in mechanics. Which one we need will depend on which angle we look at, and what we want to do.
For example, if you have the angle between two vectors, and you want to know how much of one is in the same direction as the other, you will need cosine. If you have the angle between two vectors and you want to know how much of one is perpendicular to the other you will need sine [and that’s what we’re using in F = ILB sin(angle)].
Similarly, if you have the other angle in the right-angle triangle (where one side is one of your vectors, and the longest side is the other), you’d need sine if you wanted how much of them is in the same direction, and cosine if you wanted how much is in the opposite direction [which is our flux = BA cos (angle)].
Vectors make this all a lot easier. Generally the sine comes up when you have a vector “cross” product, and cosine when you have the vector “dot” product (these are the two ways of multiplying vectors together). Although sometimes differentiation is involved, which changes sines into cosines, and vice versa. If you are not comfortable with vectors, or trig geometry in general, you’ll probably need to just memorise. Explaining them in detail requires a lot of diagrams, and Reddit isn’t the best place for that.
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