Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 5 - Trigonometric Functions - 5.2 Trigonometric Functions - 5.2 Exercises - Page 518: 42

Answer

$\bf{Positive}$

Work Step by Step

Let us suppose that a point P whose co-ordinates can be written as: $P(x, y)$ The signs of $x$ and $y$ in each trigonometric quadrant can be written as: Case 1: In the First Quadrant , we have $x$ is positive and $y$ is positive. Case 2: In the Second Quadrant , we have $x$ is Negative and $y$ is positive. Case 3: In the Third Quadrant , we have $x$ is Negative and $y$ is Negative. Case 4: In the Fourth Quadrant , we have $x$ is positive and $y$ is Negative. and the value of $r$ is always be positive and can be defined as: $r=\sqrt {x^2+y^2}$ Now, we will use the above information. In the First Quadrant , we have $x$ is positive and $y$ is positive. So, $\dfrac{y}{x}=\dfrac{+}{+}=Positive$ Thus, the ratio is $\bf{Positive}$
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