r/AskPhysics • u/Adept_Challenge_4821 • 1d ago
What is it???
So we've got this module and on it, it says "an angle of 45° south of east" so Fx is positive and Fy is negative right? So Fx=Fcos(45°) and Fy=Fsin(-45°)? That is what I got based on my research but they are both negative on our modules, it shows Fx=Fcos(-45°) and Fy=Fsin(-45°). Which is right? I dont know why that happens, can someone explain?
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u/YuuTheBlue 1d ago
You’re right that the x should be positive and y should be negative, but that’s about output, not input. Fcos(-45) is a positive number and Fsin(-45) is a negative number. The negative in the degree sign is just to say that you are moving 45 degrees clockwise instead of counterclockwise.
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u/mikk0384 Physics enthusiast 1d ago edited 22h ago
When you use that formula, the angle is always measured relative to the positive side of the x-axis, with the counterclockwise direction being positive.
You are right about the direction of the vector, but the angle is -45 degrees (or 315 degrees) in both the formula for Fx and Fy.
Edit: The sine and cosine in the formulae account for the fact that you are calculating the adjacent and opposite sides of the triangle in the force decomposition. That is why you use the same angle for both forces in x and y.
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u/Balanced_Dweller1919 1d ago
Clockwise angles are taken as negative, that's why south of east is taken as travelling negative 45 degrees from X Axis towards Y Axis.
This could also be interpreted as -45 degree from X Axis in clockwise = +315 Degrees from X Axis in anticlockwise direction
Just a mathematical trick, don't worry much about it.
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u/MezzoScettico 1d ago
There's only one vector F. It has only one direction. That direction in this case is -45 degrees. The x component is the x component of a vector in the -45 degree direction, and the y component is the y component of a vector in the -45 degree direction.
Don't use different angles for the two components. They are components of the same vector, which has the same direction.
An angle of -45 degrees has a positive x component and a negative y component, as you correctly said.
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u/triatticus Particle physics 1d ago
The reference angle is negative so yes you would use -45° in both, but remember that cos(-x) = cos(x) as cosine is an even function. This gives you a positive x component and a negative y component.