Find the direction angle of t= -9i+10j Round your answer to the nearest tenth of a degree

To find the direction angle \(\theta\) of the vector \(\mathbf{t} = -9\mathbf{i} + 10\mathbf{j}\), we use the following formula:

\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]

where \(x = -9\) and \(y = 10\).

However, since the vector lies in the second quadrant (negative x and positive y), the direction angle will be:

\[
\theta = \tan^{-1}\left(\frac{10}{-9}\right) + 180^\circ
\]

Now, let's calculate the angle:

\[
\theta = \tan^{-1}\left(\frac{10}{-9}\right) + 180^\circ \approx \tan^{-1}(-1.1111) + 180^\circ
\]

First, find \(\tan^{-1}(-1.1111)\):

\[
\theta \approx -48.0^\circ + 180^\circ = 132.0^\circ
\]

So, the direction angle \(\theta\) is approximately **132.0°**.

Would you like more details or have any questions? 

Here are 5 related questions for further exploration:
1. How do you calculate the magnitude of a vector given its components?
2. What is the relationship between direction angles and vector components?
3. How do direction angles change in different quadrants?
4. How can vectors be represented in polar form?
5. What is the geometric interpretation of a direction angle?

**Tip:** Remember that when finding the direction angle, the quadrant of the vector determines whether you need to adjust the angle by adding 180° or 360°.

Learn how to find the direction angle of vector t = -9i + 10j rounded to the nearest tenth of a degree. This problem involves vectors and trigonometric functions, specifically the inverse tangent formula for calculating direction angles. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation