Find tan a. V[ ? (V5, -/7)
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
![**Title: Finding the Tangent of an Angle α**
**Objective:**
Learn how to find the tangent of an angle given a point on the coordinate plane.
**Concept Overview:**
In this diagram, we are tasked with finding the tangent of the angle α, which is formed by a vector \( r \) originating from the origin and terminating at the point \((\sqrt{5}, -\sqrt{7})\).
**Diagram Explanation:**
- A coordinate plane is depicted with both horizontal and vertical axes.
- The vector \( r \) makes an angle α with the horizontal axis.
- The coordinates of the endpoint of the vector are \((\sqrt{5}, -\sqrt{7})\).
**Steps to Find \(\tan \alpha\):**
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side:
\[
\tan \alpha = \frac{\text{Opposite}}{\text{Adjacent}}
\]
For a point \((x, y)\),
- \(\tan \alpha = \frac{y}{x}\)
Plugging in the coordinates:
- \(\tan \alpha = \frac{-\sqrt{7}}{\sqrt{5}}\)
**Conclusion:**
The tangent of angle α is \(\frac{-\sqrt{7}}{\sqrt{5}}\), which simplifies the trigonometric analysis of the vector in relation to the coordinate plane. Understanding this ratio is fundamental in relating algebraic expressions to geometric representations in trigonometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f2c9438-5a89-4288-b691-8fe1dc913be9%2F45983d51-3efe-4b67-80e7-ee224c930312%2Fholypvm_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Finding the Tangent of an Angle α**
**Objective:**
Learn how to find the tangent of an angle given a point on the coordinate plane.
**Concept Overview:**
In this diagram, we are tasked with finding the tangent of the angle α, which is formed by a vector \( r \) originating from the origin and terminating at the point \((\sqrt{5}, -\sqrt{7})\).
**Diagram Explanation:**
- A coordinate plane is depicted with both horizontal and vertical axes.
- The vector \( r \) makes an angle α with the horizontal axis.
- The coordinates of the endpoint of the vector are \((\sqrt{5}, -\sqrt{7})\).
**Steps to Find \(\tan \alpha\):**
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side:
\[
\tan \alpha = \frac{\text{Opposite}}{\text{Adjacent}}
\]
For a point \((x, y)\),
- \(\tan \alpha = \frac{y}{x}\)
Plugging in the coordinates:
- \(\tan \alpha = \frac{-\sqrt{7}}{\sqrt{5}}\)
**Conclusion:**
The tangent of angle α is \(\frac{-\sqrt{7}}{\sqrt{5}}\), which simplifies the trigonometric analysis of the vector in relation to the coordinate plane. Understanding this ratio is fundamental in relating algebraic expressions to geometric representations in trigonometry.
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