Find the direction angle of w=(-3,-3) *Round* *your answer to the nearest tenth of a* *degree.*

To find the direction angle \(\theta\) of the vector \(\mathbf{w} = (-3, -3)\), we use the formula:

\[
\theta = \arctan\left(\frac{y}{x}\right)
\]

where \(x = -3\) and \(y = -3\).

\[
\theta = \arctan\left(\frac{-3}{-3}\right) = \arctan(1)
\]

The arctangent of 1 is \(45^\circ\). However, since both \(x\) and \(y\) are negative, the vector lies in the third quadrant, where the angle is \(180^\circ + 45^\circ\).

So, the direction angle is:

\[
\theta = 225^\circ
\]

Rounded to the nearest tenth of a degree, the direction angle is:

\[
\theta = 225.0^\circ
\]

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you find the magnitude of vector \(\mathbf{w} = (-3, -3)\)?
2. What would be the direction angle if the vector were \((3, -3)\)?
3. How does the quadrant affect the calculation of the direction angle?
4. What is the direction angle of a vector \(\mathbf{v} = (-2, 2)\)?
5. How do you convert a direction angle from degrees to radians?

**Tip:** The direction angle is always measured counterclockwise from the positive x-axis. Adjust it based on the vector's quadrant.

Learn how to find the direction angle of the vector (-3, -3) using trigonometric principles. This problem involves calculating the angle formed by a vector in a Cartesian coordinate system, rounded to the nearest tenth of a degree.

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