# Determining x & y Components of Vectors in xy Plane

• Susanem7389
In summary: I think I got it. In summary, the x component of the velocity vector is 25 m/s and the y component is 40 lb. The x component of the force vector is 120 degree counterclockwise from the -y direction and the y component of the force vector is 120 degree counterclockwise from the -x direction.
Susanem7389
I am having some trouble with this question.

Determine the x and y components of the following two vectors in the xy plane. (A) A 25- m/s velocity vector that makes an angle of 40 degree counterclockwise from the -x direction. (B) A 40lb force vector that makes an angle of 120 degree counterclockwise from the -y direction.

Hi Susanem7389!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

I drew the graph and and tried the Ax=AcosDegree and Ay=AsinDegree, however I never get the correct answer and I'm not sure how to go about getting the answer when it is in the -x direction since the equation two lines before is for the +x direction.

Susanem7389 said:
… I'm not sure how to go about getting the answer when it is in the -x direction since the equation two lines before is for the +x direction.

use sin(180º - θ) = sinθ, cos(180º - θ) = -cosθ

Okay. Thank you. It is correct. So if you have a vector that is in the -x direction, then you could you the formula that you gave? Also, what about if you have a vector the is in the -y direction and +y direction and need to use the Ax=A sin Degree and Ay= A cos Degree in the +x direction, how would you go about solving those? I'm new to vectors and trying to figure out how to do them.

Susanem7389 said:
So if you have a vector that is in the -x direction, then you could you the formula that you gave? Also, what about if you have a vector the is in the -y direction and +y direction and need to use the Ax=A sin Degree and Ay= A cos Degree in the +x direction, how would you go about solving those?

erm … sorry … i don't understand any of that

can you please write it out again?​

Sure. Sorry about the confusion. I am just learning vectors and I'm trying to understand how to find the components. The equation in the book for finding components is Ax=Acosθ and Ay=Asinθ. However that is only the case if the vector is in the +x direction. How would you go about finding the component if the vector is in the -y and +y direction? Also, if you have a vector that is in the -x direction, do I always use sin(180º - θ) = sinθ, cos(180º - θ) = -cosθ to find the answer.

still not sure what you mean by the +y and -y directions …

anyway, the formulas Ax=Acosθ and Ay=Asinθ work for any vector at any angle …

you simply have to understand how to find sin and cos for angles between 90º and 360º.

Yes, I meant about the third and fourth quadrants. Thank you for all your help. Do you have any more information or know of any websites that could help me understand how to find sin and cos for angles between 90 and 360 degree?

Susanem7389 said:
Do you have any more information or know of any websites that could help me understand how to find sin and cos for angles between 90 and 360 degree?

sorry, i don't know of anything that would help …

but it's pretty obvious what the angle is in any particular case, just by drawing it

Okay thank you.

## What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. In the context of determining x and y components, a vector is often represented as an arrow pointing from the origin to a specific point in the xy plane.

## How do you determine the x and y components of a vector?

To determine the x and y components of a vector, you can use the trigonometric functions sine and cosine. The x component is equal to the magnitude of the vector multiplied by the cosine of the angle it makes with the x-axis, while the y component is equal to the magnitude multiplied by the sine of the angle.

## What is the difference between magnitude and direction of a vector?

The magnitude of a vector refers to its size or length, while the direction refers to the angle it makes with a specific reference axis. In the xy plane, the reference axis is usually the x-axis, and the direction is measured counterclockwise from the positive x-axis.

## Why is it important to determine the x and y components of a vector?

Determining the x and y components of a vector is important because it allows us to break down a complex vector into simpler components that are easier to work with. This is especially useful in physics and engineering when dealing with forces and motion in multiple directions.

## Can the x and y components of a vector be negative?

Yes, the x and y components of a vector can be negative. Negative components indicate that the vector is pointing in the opposite direction of the positive axis. For example, a vector with a negative x component will point to the left of the origin in the xy plane.

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