A vector is 160 degrees counterclockwise from the positive x axis

If a vector is \(160^\circ\) counterclockwise from the positive x-axis, this means that the vector is located in the second quadrant of the coordinate system. 

### Key Details:
1. **Angle Reference**: 
   - The angle is measured from the positive x-axis moving counterclockwise.
   - \(0^\circ\) corresponds to the positive x-axis.
   - \(90^\circ\) corresponds to the positive y-axis.
   - \(180^\circ\) corresponds to the negative x-axis.

2. **Component Breakdown**:
   - The vector can be broken down into its x and y components using trigonometric functions.

### Components:
- **X-component**: This represents how much of the vector lies along the x-axis.
  \[
  V_x = V \cos \theta
  \]
  Here, \(\theta = 160^\circ\). Since \(160^\circ\) is in the second quadrant, \(\cos(160^\circ)\) will be negative.
  
- **Y-component**: This represents how much of the vector lies along the y-axis.
  \[
  V_y = V \sin \theta
  \]
  For \(160^\circ\), \(\sin(160^\circ)\) will be positive.

### Summary:
- The x-component will be negative, indicating a leftward direction along the x-axis.
- The y-component will be positive, indicating an upward direction along the y-axis.

Would you like more details on this, or do you have any specific questions?

Here are 5 related questions for practice:
1. What are the components of a vector at \(45^\circ\) counterclockwise from the positive x-axis?
2. How does the angle of a vector affect the signs of its x and y components?
3. What quadrant is a vector in if it is at \(220^\circ\) counterclockwise from the positive x-axis?
4. How would you find the magnitude of a vector given its components?
5. What is the angle of a vector if its y-component is three times its x-component?

**Tip**: To find which quadrant a vector is in, remember that angles from \(0^\circ\) to \(90^\circ\) are in the first quadrant, \(90^\circ\) to \(180^\circ\) are in the second, \(180^\circ\) to \(270^\circ\) are in the third, and \(270^\circ\) to \(360^\circ\) are in the fourth.

Understand how to determine vector components at 160 degrees counterclockwise from the positive x-axis using trigonometric functions. Explore the breakdown of vector components along the x and y axes in the second quadrant.

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