Fx, Fy = <em>F</em> cos θ, <em>F</em> sin θ
<h3>
Further explanation</h3>
This is a fundamental problem with vector components.
- A vector quantity is some quantities that have the magnitude and a direction. For example, all forces or momentums are vectors.
- Whereas, a scalar quantity only has magnitude. For example, all forms of energy are scalars.
The list below shows some recognized methods to represent a vector. i.e., a force.
![\boxed{ \ \textit{\textbf{F}}, \vec{F}, \bar{F} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%5Ctextit%7B%5Ctextbf%7BF%7D%7D%2C%20%5Cvec%7BF%7D%2C%20%5Cbar%7BF%7D%20%5C%20%7D)
It is possible to split one vector into two vectors. This process is called resolving and the vectors that we get are called the components of the original vector.
Vector problems can always be solved by using the mathematics of trigonometry, i.e., the functions of sine or cosine. This is particularly appropriate when resolving.
By using the cartesian coordinate system, see the attachment on how to calculate the values of either these components.
- Horizontal component:
![\boxed{ \ F_x = \textit{\textbf{F}}\ cos \ \theta \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20F_x%20%3D%20%5Ctextit%7B%5Ctextbf%7BF%7D%7D%5C%20cos%20%5C%20%5Ctheta%20%5C%20%7D)
- Vertical component:
![\boxed{ \ F_y = \textit{\textbf{F}} \ sin \ \theta \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20F_y%20%3D%20%5Ctextit%7B%5Ctextbf%7BF%7D%7D%20%5C%20sin%20%5C%20%5Ctheta%20%5C%20%7D)
Here, the angle between the vector <em>F</em> and the horizontal axis we call θ (theta).
<u>As a reminder:</u>
<h3>Learn more</h3>
- Finding the acceleration between two vectors brainly.com/question/6268248
- A correct representation of 0.000025 in scientific notation brainly.com/question/2261308
- The theoretical density of platinum which has the FCC crystal structure brainly.com/question/5048216
Keywords: express Fx and Fy, in terms of the length of the vector F, and the angle θ, with the components, separated by a comma, resolving, split, horizontal, vertical, angle, theta, sine, cosine, trigonometry, cartesian coordinate system