Finding X & Y Components of Vectors

In summary, the X and Y components of a vector are two perpendicular parts that make up the full vector. They can be found using trigonometric functions and are important for understanding the direction and magnitude of a vector. A vector can have negative X or Y components, and the components have a relationship with the vector's magnitude according to the Pythagorean theorem.
  • #1
Coder74
20
0
Im learning about how to find the x and y components of a vector, but I wanted to verify if I'm on the right track..

Ax=A cos(\theta) <-- solving for x

Ay=A sin(\theta) <-- solving for y

So if a vector is 9.55m long and points in a -48.0 degree direction.

Is it Ay= 9.55 sin(-48.0)=7.3
 
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  • #2
I get:

\(\displaystyle A_y=9.55\sin\left(-48^{\circ}\right)\text{ m}=-9.55\sin\left(48^{\circ}\right)\text{ m}\approx-7.10\text{ m}\)

Your calculator is in radian mode...and don't forget $\sin(-x)=-\sin(x)$...:D
 

FAQ: Finding X & Y Components of Vectors

What are X and Y components of a vector?

The X and Y components of a vector are the two perpendicular parts of the vector that, when added together, make up the full vector. The X component is the horizontal part and the Y component is the vertical part.

How do you find the X and Y components of a vector?

To find the X and Y components of a vector, you can use the trigonometric functions sine and cosine. The X component can be found by multiplying the magnitude of the vector by the cosine of the angle between the vector and the positive X axis. The Y component can be found by multiplying the magnitude of the vector by the sine of the angle.

Why is it important to find the X and Y components of a vector?

Finding the X and Y components of a vector is important because it allows us to break down a vector into its individual parts and understand its direction and magnitude in a more meaningful way. It also helps in performing vector operations such as addition, subtraction, and multiplication.

Can a vector have negative X or Y components?

Yes, a vector can have negative X or Y components. The sign of the components depends on the direction of the vector. For example, if a vector is pointing in the negative X direction, its X component will be negative.

What is the relationship between the X and Y components of a vector and its magnitude?

The X and Y components of a vector, when squared and added together, equal the square of the vector's magnitude. This relationship can also be represented using the Pythagorean theorem: c2 = a2 + b2, where c is the magnitude of the vector, and a and b are the X and Y components, respectively.

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