Trigonometry (10th Edition)

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

Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises: 71

Answer

$\sin\theta=\frac{y}{r}=\frac{\sqrt 5}{7}$ $\cos\theta=\frac{x}{r}=\frac{\sqrt {44}}{7}$ $\tan\theta=\frac{y}{x}=\frac{\sqrt 5}{\sqrt{44}}=\frac{\sqrt {220}}{44}$ $\cot\theta=\frac{x}{y}=\frac{\sqrt {44}}{\sqrt 5}=\frac{\sqrt {220}}{ 5}$ $\sec\theta=\frac{r}{x}=\frac{7}{\sqrt {44}}\frac{7\sqrt {44}}{44}$ $\csc\theta=\frac{r}{y}=\frac{7}{\sqrt 5}=\frac{7\sqrt 5}{5}$

Work Step by Step

1.Angle in quadrant I, x is positive and y is negative Given values $y=\sqrt 5$ and $r=7$ 2. Using given values and distance formula, we can find the x $7=\sqrt {(x)^{2}+(\sqrt 5)^{2}}$ $49=5+x^{2}$ $x=\sqrt {44}$ 3.Plug the values to find trig functions $\sin\theta=\frac{y}{r}=\frac{\sqrt 5}{7}$ $\cos\theta=\frac{x}{r}=\frac{\sqrt {44}}{7}$ $\tan\theta=\frac{y}{x}=\frac{\sqrt 5}{\sqrt{44}}=\frac{\sqrt {220}}{44}$ $\cot\theta=\frac{x}{y}=\frac{\sqrt {44}}{\sqrt 5}=\frac{\sqrt {220}}{ 5}$ $\sec\theta=\frac{r}{x}=\frac{7}{\sqrt {44}}\frac{7\sqrt {44}}{44}$ $\csc\theta=\frac{r}{y}=\frac{7}{\sqrt 5}=\frac{7\sqrt 5}{5}$
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