Q. 18 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. 18 (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 $t$ .
$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

Short Answer

Expert verified

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

$\begin{matrix} \sin t = \frac{\sqrt{2}}{2} \\ \cos t = \frac{\sqrt{2}}{2} \\ \tan t = 1 \\ \csc t = \sqrt{2} \\ \sec t = \sqrt{2} \\ \cot t = 1 \end{matrix}$

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, $P (x, y) = P (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

Substitute these values in the six trigonometric functions and simplify.

Find $\sin t$ .

$\sin t = y \sin t = \frac{\sqrt{2}}{2}$

Find $\cos t$ .

$\cos t = x \cos t = \frac{\sqrt{2}}{2}$

Find $\tan t$ .

$\tan t = \frac{y}{x} \tan t = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \tan t = 1$

Evaluate.

Find $c s c t$ .

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

Find $s e c t$ .

$s e c t = \frac{1}{x} s e c t = \frac{1}{\frac{\sqrt{2}}{2}} s e c t = \frac{2}{\sqrt{2}} s e c t = \sqrt{2}$

Find $c o t t$ .

$c o t t = \frac{x}{y} c o t t = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} c o t t = 1$

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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 $t$ .
$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

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.22,22.

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

Discrete Mathematics

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

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 $t$ .
$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .