Trigonometry (10th Edition)

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

Chapter 1 - Review Exercises: 41

Answer

$\sin\theta=\frac{y}{r}=\frac{-\sqrt {39}}{8}$ $\cos\theta=\frac{x}{r}=\frac{-5}{8}=$ $\csc\theta=\frac{r}{y}=\frac{8}{-\sqrt {39}}=-\frac{8\sqrt {39}}{39}$ $\sec\theta=\frac{r}{x}=\frac{8}{-5}$ $\tan\theta=\frac{y}{x}=\frac{-\sqrt {39}}{-5}=\frac{\sqrt {39}}{5}$ $\cot\theta=\frac{x}{y}=\frac{-5}{-\sqrt {34}}=\frac{5\sqrt {39}}{39}$

Work Step by Step

We know that angle in III quadrant will have negative x and y values, therefore we get following values from the cosine $x=-5; r=8$, so lets find y: $x^{2}+y^{2}=r^{2}$ $5^{2}+(y)^{2}=8^{2}$ $y^{2}+25=64$ $x^{2}=39$ (since we know that x is negative) $x=\sqrt {39}$
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