**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.

Answered: Image /qna-images/answer/45983d51-3efe-4b67-80e7-ee224c930312.jpg

Answered: Find tan a. V[ ? (V5, -/7)

Find tan a. V[ ? (V5, -/7)

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°.

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