Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 11 - Section 11.3 - The Tangent Ratio and Other Ratios - Exercises - Page 519: 10


$\sin\alpha=\frac{x}{\sqrt{x^{2}+4}}$ $\cos\alpha=\frac{2}{\sqrt{x^{2}+4}}$ $\tan\alpha=\frac{x}{2}$ $\csc\alpha=\frac{\sqrt{x^{2}+4}}{x}$ $\sec\alpha=\frac{\sqrt{x^{2}+4}}{2}$ $\cot\alpha=\frac{2}{x}$

Work Step by Step

Let $l$ be the length of the side with an unknown length. $l=\sqrt{x^{2}+2^{2}}$ $l=\sqrt{x^{2}+4}$ $\sin\alpha=\frac{opposite}{hypotenuse}=\frac{x}{\sqrt{x^{2}+4}}$ $\cos\alpha=\frac{adjacent}{hypotenuse}=\frac{2}{\sqrt{x^{2}+4}}$ $\tan\alpha=\frac{opposite}{adjacent}=\frac{x}{2}$ $\csc\alpha=\frac{hypotenuse}{opposite}=\frac{\sqrt{x^{2}+4}}{x}$ $\sec\alpha=\frac{hypotenuse}{adjacent}=\frac{\sqrt{x^{2}+4}}{2}$ $\cot\alpha=\frac{adjacent}{opposite}=\frac{2}{x}$
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