Find tan a. (-15, 8) r a Type + or - [?
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
Hey what’s the answer to this
![**Title: Finding the Tangent of an Angle in a Coordinate System**
**Objective:**
Learn how to find the tangent of an angle formed by a line with the horizontal axis in a coordinate system.
**Problem:**
Find \( \tan \alpha \).
**Diagram:**
- A Cartesian coordinate system is presented with the x-axis (horizontal) and y-axis (vertical).
- A line segment \( r \) originates from the origin (0, 0) and passes through the point (-15, 8), creating an angle \( \alpha \) with the positive x-axis.
Point:
- The coordinates of the point are given as (-15, 8).
**Instruction:**
Type + or -
**Explanation:**
To find \( \tan \alpha \):
- Recall that \( \tan \alpha \) in a right-angled triangle formed in the coordinate system is given by the ratio of the opposite side to the adjacent side.
- The opposite side corresponds to the y-coordinate (8).
- The adjacent side corresponds to the x-coordinate (-15).
Thus,
\[ \tan \alpha = \frac{8}{-15} = -\frac{8}{15} \]
**Answer Input Field:**
An input field labeled “Enter” is provided to input the sign of the calculated tangent value.
**Solution Steps:**
1. Identify the coordinates of the given point (-15, 8).
2. Determine the signs of the coordinates.
3. Calculate \( \tan \) by taking the ratio of the y-coordinate to the x-coordinate.
4. Input the sign (+ or -) of the calculated value in the provided field.
**Note:** The result indicates the direction of the angle and its position relative to the axes.
**Usage Rights:**
© 2003 - 2023 International Academy of Science. All Rights Reserved.
**Additional Resources:**
You may find PDFs and other additional learning materials on the website.
---
By following these steps, students will understand how to approach finding the tangent of an angle formed by a line with the horizontal axis in a coordinate system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59dc451e-d6f8-4dd4-9faf-549af2b24cc3%2Fe3ec8927-b9eb-4a48-a5e8-4efec5300a4d%2Fspjc34e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Finding the Tangent of an Angle in a Coordinate System**
**Objective:**
Learn how to find the tangent of an angle formed by a line with the horizontal axis in a coordinate system.
**Problem:**
Find \( \tan \alpha \).
**Diagram:**
- A Cartesian coordinate system is presented with the x-axis (horizontal) and y-axis (vertical).
- A line segment \( r \) originates from the origin (0, 0) and passes through the point (-15, 8), creating an angle \( \alpha \) with the positive x-axis.
Point:
- The coordinates of the point are given as (-15, 8).
**Instruction:**
Type + or -
**Explanation:**
To find \( \tan \alpha \):
- Recall that \( \tan \alpha \) in a right-angled triangle formed in the coordinate system is given by the ratio of the opposite side to the adjacent side.
- The opposite side corresponds to the y-coordinate (8).
- The adjacent side corresponds to the x-coordinate (-15).
Thus,
\[ \tan \alpha = \frac{8}{-15} = -\frac{8}{15} \]
**Answer Input Field:**
An input field labeled “Enter” is provided to input the sign of the calculated tangent value.
**Solution Steps:**
1. Identify the coordinates of the given point (-15, 8).
2. Determine the signs of the coordinates.
3. Calculate \( \tan \) by taking the ratio of the y-coordinate to the x-coordinate.
4. Input the sign (+ or -) of the calculated value in the provided field.
**Note:** The result indicates the direction of the angle and its position relative to the axes.
**Usage Rights:**
© 2003 - 2023 International Academy of Science. All Rights Reserved.
**Additional Resources:**
You may find PDFs and other additional learning materials on the website.
---
By following these steps, students will understand how to approach finding the tangent of an angle formed by a line with the horizontal axis in a coordinate system.
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