Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 11 - Section 11.3 - The Tangent Ratio and Other Ratios - Exercises: 8

Answer

$\sin\alpha=\frac{y}{\sqrt{x^{2}+y^{2}}}$ $\cos\alpha=\frac{x}{\sqrt{x^{2}+y^{2}}}$ $\tan\alpha=\frac{y}{x}$ $\csc\alpha=\frac{\sqrt{x^{2}+y^{2}}}{y}$ $\sec\alpha=\frac{\sqrt{x^{2}+y^{2}}}{x}$ $\cot\alpha=\frac{x}{y}$

Work Step by Step

$\sin\alpha=\frac{opposite}{hypotenuse}=\frac{y}{\sqrt{x^{2}+y^{2}}}$ $\cos\alpha=\frac{adjacent}{hypotenuse}=\frac{x}{\sqrt{x^{2}+y^{2}}}$ $\tan\alpha=\frac{opposite}{adjacent}=\frac{y}{x}$ $\csc\alpha=\frac{hypotenuse}{opposite}=\frac{\sqrt{x^{2}+y^{2}}}{y}$ $\sec\alpha=\frac{hypotenuse}{adjacent}=\frac{\sqrt{x^{2}+y^{2}}}{x}$ $\cot\alpha=\frac{adjacent}{opposite}=\frac{x}{y}$
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