Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 1 - Test - Page 44: 16

Answer

We can see a sketch of the least positive angle $\theta$ below. We can find the trigonometric values: $sin ~\theta = \frac{y}{r} = \frac{-3}{5}$ $cos ~\theta = \frac{x}{r} = \frac{-4}{5}$ $tan ~\theta = \frac{y}{x} = \frac{3}{4}$ $csc ~\theta = \frac{r}{y} = \frac{5}{-3}$ $sec ~\theta = \frac{r}{x} = \frac{5}{-4}$ $cot ~\theta = \frac{x}{y} = \frac{4}{3}$

Work Step by Step

$3x-4y=0$ $\frac{y}{x} = \frac{3}{4} = \frac{-3}{-4}$ Since $x \leq 0$, we can let $x=-4$ and $y=-3$ Then $r = \sqrt{(-4)^2+(-3)^2} = 5$ We can see a sketch of the least positive angle $\theta$ below. We can find the trigonometric values: $sin ~\theta = \frac{y}{r} = \frac{-3}{5}$ $cos ~\theta = \frac{x}{r} = \frac{-4}{5}$ $tan ~\theta = \frac{y}{x} = \frac{3}{4}$ $csc ~\theta = \frac{r}{y} = \frac{5}{-3}$ $sec ~\theta = \frac{r}{x} = \frac{5}{-4}$ $cot ~\theta = \frac{x}{y} = \frac{4}{3}$
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