Q. 20 In problems 13-20, Px,y聽is the ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 20 (page 380)

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .
$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .

Short Answer

Expert verified

The exact values of the six trigonometric functions of $t$ for $(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ are:

$\begin{matrix} \sin t = - \frac{2}{3} \\ \cos t = - \frac{\sqrt{5}}{3} \\ \tan t = \frac{2}{5} \sqrt{5} \\ \csc t = - \frac{3}{2} \\ \sec t = - \frac{3}{5} \sqrt{5} \\ \cot t = \frac{\sqrt{5}}{2} \end{matrix}$

Step by step solution

Definitions.

For a point $P (x, y)$ on a unit circle that corresponds to $t$ , the six trigonometric functions are defined as follows:

$\begin{matrix} \sin t = y \\ \cos t = x \\ \tan t = \frac{y}{x} \\ \csc t = \frac{1}{y} \\ \sec t = \frac{1}{x} \\ \cot t = \frac{x}{y} \end{matrix}$

Evaluate

Here, $P (x, y) = P (- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .

Substitute these values in the six trigonometric functions and simplify.

Find $\sin t$ .

$\sin t = y \sin t = - \frac{2}{3}$

Find $\cos t$ .

$\cos t = x \cos t = - \frac{\sqrt{5}}{3}$

Find $\tan t$ .

$\tan t = \frac{y}{x} \tan t = \frac{- \frac{2}{3}}{- \frac{\sqrt{5}}{3}} \tan t = \frac{2}{\sqrt{5}} \tan t = \frac{2}{5} \sqrt{5}$

Evaluate.

Find $c s c t$ .

$c s c t = \frac{1}{y} c s c t = \frac{1}{- \frac{2}{3}} c s c t = - \frac{3}{2}$

Find $s e c t$ .

$s e c t = \frac{1}{x} s e c t = \frac{1}{- \frac{\sqrt{5}}{3}} s e c t = - \frac{3}{\sqrt{5}} s e c t = - \frac{3}{5} \sqrt{5}$

Find $c o t t$ .

$c o t t = \frac{x}{y} c o t t = \frac{- \frac{\sqrt{5}}{3}}{- \frac{2}{3}} c o t t = \frac{\sqrt{5}}{2}$

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91影视

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .
$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .

Short Answer

Step by step solution

Definitions.

Evaluate

Evaluate.

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91影视

In problems 13-20, Px,yis the point on the unit circle that corresponds to a real number t. Find the exact values of the six trigonometric functions of t.-53,-23.

Short Answer

Step by step solution

Definitions.

Evaluate

Evaluate.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

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Discrete Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .
$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .