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.
In: 4
In these cases you are dealing with sin and cos because you are essentially comparing the magnitude of two vectors.
As a simpler example, consider a cube sliding down a wedge. Gravity creates a directional force straight down. But the object can’t go straight down because of the wedge. So wedge essentially redirects that force in a different direction by some angle.
From these two vectors/directions we can construct a right-angled triangle with the primary force (gravity) as the hypotenuse and one of the legs being the wedge itself. What we want to know is the length (magnitude) of the leg of the triangle that corresponds to the wedge.
Illustration:
[https://i.imgur.com/Ljn09Wa.png](https://i.imgur.com/Ljn09Wa.png)
For this we would use sin. Why? Because:
sin(theta) = opposite/hypotenuse
And the side opposite the angle, theta is what we want to figure out. Since we know the angle of the wedge (theta) and the force due to gravity (Fg) we can figure out the opposite side (net force) using sin.
If, instead, we measured the angle of the wedge from the other angle, we’d use cos, because then the “net force” side would be adjacent to the angle.
So the choice of cos vs. sin depends on how the different vectors (directions of force) relate to teach other.
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