Absolutely! Your question is about finding **Hx** and **Hy**—these usually refer to the magnetic field components, but they could represent any physical quantity’s components along the x and y axes. I’ll assume you’re dealing with vector components (like magnetic fields, electric fields, etc.). If you have a specific vector or context, let me know! Let’s proceed step-by-step as you requested: --- ### **Step 1: Introduction to the Concept** Whenever a vector is given (say **H**), it can be split into components along the x-axis (**Hx**) and y-axis (**Hy**). These components show how much of the vector points in each direction. This process is called "resolving the vector into components." It's a fundamental concept in physics and engineering because it helps us analyze forces, fields, or any vector quantities in two or three dimensions. --- ### **Step 2: Finding Hx** Suppose the vector **H** has a magnitude |H| and makes an angle θ with the x-axis. - The component along the x-axis (**Hx**) is found using: \[ H_x = |H| \cdot \cos(\theta) \] **Explanation:** Cosine gives the ratio of the adjacent side (x-component) to the hypotenuse (the magnitude of the vector) in a right triangle formed by the vector and the axes. --- ### **Step 3: Finding Hy** - The component along the y-axis (**Hy**) is found using: \[ H_y = |H| \cdot \sin(\theta) \] **Explanation:** Sine gives the ratio of the opposite side (y-component) to the hypotenuse (the magnitude of the vector). --- ### **Step 4: Final Answer in Few Sentences** **Final Answer:** To find the x and y components of a vector **H**, multiply its magnitude by the cosine of its angle with the x-axis for **Hx**, and by the sine of the angle for **Hy**: \[ H_x = |H| \cos(\theta), \quad H_y = |H| \sin(\theta) \] --- ### **Step 5: Summary of What We Did** **Summary:** First, we introduced the idea of vector components. Then, we explained how to calculate **Hx** and **Hy** using trigonometry based on the vector's magnitude and direction. Finally, we summarized the process with the key formulas. --- **If you have specific numbers or a diagram, let me know for a worked-out example!**