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To calculate the \( x \) and \( y \) components of the vector, we need to apply the following formulas based on the vector's magnitude and direction:

- \( x = r \cdot \cos(\theta) \)
- \( y = r \cdot \sin(\theta) \)

Where:
- \( r \) is the magnitude of the vector (given as 35).
- \( \theta \) is the angle the vector makes with the positive \( x \)-axis (given as 54°).

Since the vector is pointing downward and to the left, its \( x \)-component will be negative and its \( y \)-component will also be negative.

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Here are some follow-up questions you might explore:
1. How do we determine which trigonometric functions to use for vector components?
2. What does it mean when the \(x\) and \(y\) components are negative?
3. How can you verify the direction of a vector's components based on its quadrant?
4. How does the angle relative to the positive \(x\)-axis affect the \(x\) and \(y\) values?
5. What is the importance of rounding intermediate results in calculations?

**Tip**: Always check the vector’s quadrant when determining the sign of its components!

Calculate the x and y components of the vector given. The vector has a magnitude of 35 and makes a 54° angle with the x-axis. Round your responses to the nearest hundredth.

Learn how to decompose a vector with a magnitude of 35 and a 54° angle into its x and y components using trigonometric functions. This problem involves applying the cosine and sine functions to determine the horizontal and vertical components, rounding results to the nearest hundredth.

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