Q.50 Find the exact value of each of ... [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.50 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃$
$\sin 胃 = \frac{- 2}{3}, 蟺 < 胃 < \frac{3 蟺}{2}$

Short Answer

Expert verified

The values are

$\cos 胃 = \frac{- \sqrt{5}}{3}, c s c 胃 = \frac{- 3}{2}, s e c 胃 = \frac{- 3}{\sqrt{5}}, \tan 胃 = \frac{2}{\sqrt{5}}, c o t 胃 = \frac{\sqrt{5}}{2}$

Step by step solution

.Given information

$\sin 胃 = \frac{- 2}{3}, 蟺 < 胃 < \frac{3 蟺}{2}$ is given.

we have to find the exact value of each of the remaining trigonometric functions

Step 2.Finding the value of cosθ

$S i n c e \sin^{2} 胃 + \cos^{2} 胃 = 1, h e r e \sin 胃 = \frac{- 2}{3} \cos 胃 = 卤 \sqrt{1 - \sin^{2} 胃}, h e r e 胃 l i e s o n 蟺 < 胃 < \frac{3 蟺}{2} s o \sin 胃 i s o n t h i r d q u a d r a n t a n d a l l o t h e r e x c e p t \tan 胃 a n d c o t 胃 a r e w i l l b e n e g a t i v e . h e n c e \cos 胃 = \sqrt{1 - \sin^{2} 胃} = - \sqrt{1 - \frac{{(- 2)}^{2}}{3^{2}}} = - \sqrt{1 - \frac{4}{9}} = - \sqrt{\frac{5}{9}} = \frac{- \sqrt{5}}{3}$

Step 3. Find the values ofcscθ and secθ

$In this question 肠蝉肠胃 = \frac{1}{蝉颈苍胃} = \frac{1}{- \frac{2}{3}}, 蝉颈苍胃 = - \frac{2}{3} = - \frac{3}{2} 肠辞蝉胃 = \frac{- \sqrt{5}}{3}, then 蝉别肠胃 = \frac{1}{肠辞蝉胃} = \frac{1}{\frac{- \sqrt{5}}{3}} = \frac{- 3}{\sqrt{5}}$

Step 4. Finding the value of tan θ and cotθ

$w e k n o w t h a t \tan 胃 = \frac{\sin 胃}{\cos 胃}, \sin 胃 = \frac{- 2}{3} a n d \cos 胃 = \frac{- \sqrt{5}}{3} = \frac{\frac{- 2}{3}}{\frac{- \sqrt{5}}{3}} = \frac{2}{\sqrt{5}} c o t 胃 = \frac{1}{\tan 胃} = \frac{1}{\frac{2}{\sqrt{5}}} = \frac{\sqrt{}}{2}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find the exact value of each of the remaining trigonometric functions of $胃$
$\sin 胃 = \frac{- 2}{3}, 蟺 < 胃 < \frac{3 蟺}{2}$

Short Answer

Step by step solution

.Given information

Step 2.Finding the value of cosθ

Step 3. Find the values ofcscθ and secθ

Step 4. Finding the value of tan θ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Logic and Functions

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Find the exact value of each of the remaining trigonometric functions of 胃sin胃=-23,蟺<胃<3蟺2

Short Answer

Step by step solution

.Given information

Step 2.Finding the value of cosθ

Step 3. Find the values ofcscθ and secθ

Step 4. Finding the value of tan θ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Logic and Functions

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃$
$\sin 胃 = \frac{- 2}{3}, 蟺 < 胃 < \frac{3 蟺}{2}$