# Vector Components

1. Feb 16, 2009

### Susanem7389

Determine the x and y components. A 40 lb force vector that makes an angle of 120 degree counterclockwise from the -y direction.

I did Ax= (40)(-cos120 degree) and Ay= (40)(sin120 degree)

I got the right answer, I just want to make sure that this is the correct way of solving the problem.

2. Feb 16, 2009

### AEM

I read your earlier thread with Tiny_Tim and noticed that you wanted a rule as to when to use the formulas he suggested. When I was teaching, I used to tell my students to draw a careful diagram and label the angles the vector makes with each axis and work then use trigonometry to find the projection of the vector on to the axes. I think that way you will make fewer mistakes.

3. Feb 16, 2009

### Susanem7389

Okay. Thank you. Also, was the way I solved the problem correct?

4. Feb 16, 2009

### AEM

Well, you said that you got the right answer, but I'm puzzled. Isn't your vector in the first quadrant making a 30 degree angle with the x axis?

Your solution is appropriate for a vector that makes an angle of 120 degrees with the Positive X axis.

Last edited: Feb 17, 2009
5. Feb 17, 2009

### Susanem7389

Yes, it is. I must have done something wrong with the equation. How would I fix it?

6. Feb 17, 2009

### robphy

The x-component of A is $$\hat x \cdot \vec A$$ (which is equal to $$(1)|A|\cos\theta_{\mbox{\small between \vec A and \hat x}}$$).
The y-component of A is $$\hat y \cdot \vec A$$ (which is equal to $$(1)|A|\cos\theta_{\mbox{\small between \vec A and \hat y}}$$).

You can also express the components as
$$A_x=A\cos\theta$$
$$A_y=A\sin\theta$$
where $$\theta$$ is the counterclockwise angle from the positive-x axis.
Note that this angle is in the range $$0\leq \theta < 360^\circ$$ (and so $$-1\leq \cos\theta\leq 1$$ and $$-1\leq \sin\theta\leq 1$$).

The above are the best facts to remember.
If you need to work with other angles, you need to draw a good picture and express the given angle in terms of the angles above [and possibly use some trig identities, especially if you want a general formula using some other choice of angles or axes].

So, for instance, if you are given a counterclockwise angle $$\phi$$ with respect to the -y axis, what is the corresponding counterclockwise angle $$\theta$$ from the +x-axis?

7. Feb 17, 2009

### Susanem7389

It would be the same numbers for both however the positive x direction, both the x and y component would be positive and for the negative y direction, both the x and y component would be negative. Thank you for your help.