Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.3 - Right Triangle Trigonometry - Exercise Set - Page 563: 84


a) The ratio that expresses $\sin \theta $ is $\frac{y}{r}$. b) The ratio for figure (b) is $\frac{y}{r}=\frac{4}{5}$, that is, positive.

Work Step by Step

(a) In this figure, both x and y coordinates are positive as they lie in the first quadrant; the ordinate is y and abscissa is x. $\sin \theta =\frac{y}{r}$ (b) In the second figure, we calculate the value of r as follows: $\begin{align} & r=\sqrt{{{x}^{2}}+{{y}^{2}}} \\ & r=\sqrt{{{\left( -3 \right)}^{2}}+{{4}^{2}}} \\ & r=\sqrt{9+16} \\ & r=\sqrt{25} \\ & r=5 \\ & \frac{y}{r}=\frac{4}{5} \end{align}$ Thus, the above ratio obtained is positive.
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