**Problem: Find \(\sin \alpha\).****Diagram Explanation:** The graph is on a coordinate grid with a marked point at coordinates \((- \sqrt{5}, 2)\). A line segment extends from the origin (0,0) to this point. The angle \(\alpha\) is formed between this line and the positive x-axis. The point where this line intersects the y-axis at 2 is depicted as one of the coordinates of the point.The segment's horizontal run is along the x-axis and vertical rise along the y-axis. The hypotenuse, representing the radius of the unit circle, is drawn from the origin to the point \((- \sqrt{5}, 2)\).The task is to determine \(\sin \alpha\). To compute this, we will use the definition of sine in a right triangle, where \(\sin \alpha = \frac{\text{opposite side}}{\text{hypotenuse}}\).To find the hypotenuse (\(r\)), we use the coordinates to calculate the distance:\[ r = \sqrt{(-\sqrt{5})^2 + 2^2} = \sqrt{5 + 4} = \sqrt{9} = 3 \]Thus, \(\sin \alpha = \frac{2}{3}\).

Answered: Image /qna-images/answer/93c8dd5a-71be-4e27-bd3c-ba60e8f5ffd2.jpg

Answered: Find sin a. (-/5 ,2) [ ?] 1

Find sin a. (-/5 ,2) [ ?] 1

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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