Finding A's Components: Non Graphical Solutions

[Dorita]

I was told to solve this non graphically. Can this problem be solved non graphically? If so, what are the appropriate steps involved. Really need to understand this stuff.

Vector A forms an angle θ with the positive part of the x axis. Find the components of A along x and y if:
a. |A| = 8 m, θ = 60º
b. |A| = 6 m, θ = 120 º
c. |A| = 1.2 m, θ = 225º

m denotes meters

Thank you very much for all the help. This is my first day on this forum and it's really amazing. I've learned so much just reading all the different threads.

Keep it up.

Dora

 

[Chi Meson]

There are different ways of solving for vector components; judging from the way the question is asked, the following might make the most sense.

Whenever you are dealing with the angle FROM the x-axis, the x-component of the vector will be the magnitude of the vector times the cosine of the angle; the y-component will be the magnitude times the sine of the angle.

If you later are given the angle from the y-axis, then the cosine function will give you the y component and the sine will give you the x component.

In general, the component along any axis will always be the magnitude times the cosine of the angle to that axis.

 

[Dorita]

I had to edit the question.
|A| = 8 m, θ = 60º not A = 8 m, θ = 60º

Sorry!

Dora

 

[Chi Meson]

The answer is the same. The absolute value bars around the "A" is the same thing as saying "the magnitude of vector A." In this case the magnitude is 8 m regardless of its direction .