h Find tan 3. (-3,-4) B ?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section1.8: The Coordinate Plane
Problem 7C
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Hey what’s the answer to this
![### Understanding the Tangent Function
**Objective:** Find the value of \(\tan \beta\).
#### Diagram Explanation:
The provided diagram includes the following elements:
- A coordinate plane with an origin at the intersection of the x-axis and y-axis.
- A point marked on the plane at coordinates \((-3, -4)\).
- A line stretching from the origin to the point \((-3, -4)\), forming an angle \(\beta\) with the negative x-axis.
- The hypotenuse (\(r\)) of the right triangle formed by the x-coordinate, y-coordinate, and the line from the origin to the point \((-3, -4)\), which is the radius.
#### Mathematical Context:
To find \(\tan \beta\), we can use the formula:
\[
\tan \beta = \frac{\text{opposite}}{\text{adjacent}}
\]
Here, \(\beta\) is the angle formed with the negative x-axis, the "opposite" side is the y-coordinate \((-4)\), and the "adjacent" side is the x-coordinate \((-3)\).
### Calculation:
Given point: \((-3, -4)\)
\[
\tan \beta = \frac{\text{opposite}}{\text{adjacent}}
\]
\[
\tan \beta = \frac{-4}{-3} = \frac{4}{3}
\]
#### Solution:
Therefore,
\[
\tan \beta = \frac{4}{3}
\]
Enter the value in the provided input box and press "Enter" to verify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88948349-7a3a-42b1-b43e-0f6310456bad%2F20dcb8e7-2008-4b06-8120-abe0a3c9ae18%2Fsohh9ib_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Tangent Function
**Objective:** Find the value of \(\tan \beta\).
#### Diagram Explanation:
The provided diagram includes the following elements:
- A coordinate plane with an origin at the intersection of the x-axis and y-axis.
- A point marked on the plane at coordinates \((-3, -4)\).
- A line stretching from the origin to the point \((-3, -4)\), forming an angle \(\beta\) with the negative x-axis.
- The hypotenuse (\(r\)) of the right triangle formed by the x-coordinate, y-coordinate, and the line from the origin to the point \((-3, -4)\), which is the radius.
#### Mathematical Context:
To find \(\tan \beta\), we can use the formula:
\[
\tan \beta = \frac{\text{opposite}}{\text{adjacent}}
\]
Here, \(\beta\) is the angle formed with the negative x-axis, the "opposite" side is the y-coordinate \((-4)\), and the "adjacent" side is the x-coordinate \((-3)\).
### Calculation:
Given point: \((-3, -4)\)
\[
\tan \beta = \frac{\text{opposite}}{\text{adjacent}}
\]
\[
\tan \beta = \frac{-4}{-3} = \frac{4}{3}
\]
#### Solution:
Therefore,
\[
\tan \beta = \frac{4}{3}
\]
Enter the value in the provided input box and press "Enter" to verify your answer.
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