I’m not sure what I did wrong. ### Direction Angles and Vectors**Direction angle (theta) must satisfy:**\[ 0 \leq \text{theta} < 360 \text{ degrees} \]**Problem:**What is the direction angle for the vector $\langle -4, 4\sqrt{3} \rangle$?**Solution:**The direction angle, $\theta$, is calculated as follows:$\theta = 60$ degrees.This result is provided in the input box, indicating that for the given vector, the direction angle is 60 degrees. **Details:**The direction angle $\theta$ is the angle formed between the positive x-axis and the vector in question. It is measured in a counter-clockwise direction from the x-axis. In this problem, it is indicated that the angle must be within the range of 0 to 360 degrees. By inputting the components of the vector $\langle -4, 4\sqrt{3} \rangle$ into a trigonometric calculation, we find that the angle is 60 degrees.### How to Find Direction AngleTo find the direction angle $\theta$ for any vector $\langle x, y \rangle$:1. Calculate the tangent of the angle:\[\tan(\theta) = \frac{y}{x}\]2. Use the arctangent function (inverse tangent) to find $\theta$:\[\theta = \tan^{-1}\left(\frac{y}{x}\right)\]3. Convert $\theta$ to degrees if it is in radians.4. Adjust $\theta$ based on the quadrant in which the vector lies.In this problem, the arctangent calculation directly provides the correct angle, being noted that the components of the vector determine which quadrant the vector is in, modifying $\theta$ accordingly.

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Direction angle (theta) must satisfy: 0 <= theta < 360 degrees. What is the direction angle for < -4, 4*sqrt(3) > ? theta = 60 degrees

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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I’m not sure what I did wrong.

### Direction Angles and Vectors

**Direction angle (theta) must satisfy:**

\[ 0 \leq \text{theta} < 360 \text{ degrees} \]

**Problem:**

What is the direction angle for the vector $\langle -4, 4\sqrt{3} \rangle$?

**Solution:**

The direction angle, $\theta$, is calculated as follows:

$\theta = 60$ degrees.

This result is provided in the input box, indicating that for the given vector, the direction angle is 60 degrees.

**Details:**

The direction angle $\theta$ is the angle formed between the positive x-axis and the vector in question. It is measured in a counter-clockwise direction from the x-axis. In this problem, it is indicated that the angle must be within the range of 0 to 360 degrees.

By inputting the components of the vector $\langle -4, 4\sqrt{3} \rangle$ into a trigonometric calculation, we find that the angle is 60 degrees.

### How to Find Direction Angle
To find the direction angle $\theta$ for any vector $\langle x, y \rangle$:

1. Calculate the tangent of the angle:
\[
\tan(\theta) = \frac{y}{x}
\]

2. Use the arctangent function (inverse tangent) to find $\theta$:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]

3. Convert $\theta$ to degrees if it is in radians.
4. Adjust $\theta$ based on the quadrant in which the vector lies.

In this problem, the arctangent calculation directly provides the correct angle, being noted that the components of the vector determine which quadrant the vector is in, modifying $\theta$ accordingly.

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