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To find the components of vector \(\vec{A}\), we'll use the trigonometric relations. The components of a vector can be found using the magnitude and direction of the vector:

For a vector \(\vec{A}\) with a magnitude \( A \) and an angle \(\theta\) relative to the positive x-axis:

- The x-component (\( A_x \)) is given by:  
  \[
  A_x = A \cdot \cos(\theta)
  \]

- The y-component (\( A_y \)) is given by:  
  \[
  A_y = A \cdot \sin(\theta)
  \]

### Calculating Components of \(\vec{A}\):

Given:
- Magnitude of \(\vec{A}\): \( A = 8.0 \, \text{m} \)
- Angle of \(\vec{A}\): \(\theta = 270^\circ\) (pointing directly downward on the negative y-axis).

So:

- \( A_x = 8.0 \cdot \cos(270^\circ) \)
- \( A_y = 8.0 \cdot \sin(270^\circ) \)

Let's calculate these values:The components of vector \(\vec{A}\) are approximately:

- \( A_x \approx 0 \, \text{m} \) (essentially zero due to rounding)
- \( A_y = -8.0 \, \text{m} \)

This makes sense since the vector points directly downward along the negative y-axis.

Would you like further details or have any questions? Here are some related questions to consider:

1. How do we calculate the components of other vectors (\(\vec{B}\), \(\vec{C}\), \(\vec{D}\))?
2. How do we find the resultant vector of multiple vectors?
3. What is the significance of positive and negative signs in vector components?
4. How can vector components be used in physics problems?
5. How do angles affect the direction and components of vectors?

**Tip:** When dealing with vectors, always pay attention to the angle's reference direction (e.g., counterclockwise from the positive x-axis) to ensure accurate calculations of components.

Learn how to calculate vector components using trigonometric functions with a detailed example. This problem involves finding the components of a vector given its magnitude and direction using cosine and sine functions. Suitable for high school students studying vectors and trigonometry.

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