Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 1 - Test - Page 46: 16

Answer

We can see a sketch of the least positive angle $\theta$ below. We can find the trigonometric values: $sin ~\theta = \frac{y}{r} = \frac{-3}{5}$ $cos ~\theta = \frac{x}{r} = \frac{-4}{5}$ $tan ~\theta = \frac{y}{x} = \frac{3}{4}$ $csc ~\theta = \frac{r}{y} = \frac{5}{-3}$ $sec ~\theta = \frac{r}{x} = \frac{5}{-4}$ $cot ~\theta = \frac{x}{y} = \frac{4}{3}$
1523447963

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: $sin ~\theta = \frac{y}{r} = \frac{-3}{5}$ $cos ~\theta = \frac{x}{r} = \frac{-4}{5}$ $tan ~\theta = \frac{y}{x} = \frac{3}{4}$ $csc ~\theta = \frac{r}{y} = \frac{5}{-3}$ $sec ~\theta = \frac{r}{x} = \frac{5}{-4}$ $cot ~\theta = \frac{x}{y} = \frac{4}{3}$
Small 1523447963
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.