Q.49 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.49 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃$
$\cos 胃 = \frac{- 1}{3}, \frac{蟺}{2} < 胃 < 蟺$

Short Answer

Expert verified

The values are

$\sin 胃 = \frac{2 \sqrt{2}}{3}, c s c 胃 = \frac{3}{2 \sqrt{2}}, s e c 胃 = - 3, \tan 胃 = - 2 \sqrt{2}, c o t 胃 = - \frac{1}{2 \sqrt{2}}$

Step by step solution

.Given information

$\cos 胃 = \frac{- 1}{3}, \frac{蟺}{2} < 胃 < 蟺$ is given.

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

Step 2. Finding the value sinθ

$W e k n o w t h a t \sin^{2} 胃 + \cos^{2} 胃 = 1, h e r e \cos 胃 = \frac{- 1}{3} \sin 胃 = 卤 \sqrt{1 - \cos^{2} 胃}, h e r e 胃 l i e s o n \frac{蟺}{2} < 胃 < 蟺 s o \cos 胃 i s o n s e c o n d q u a d r a n t a n d a l l o t h e r e x c e p t \sin 胃 a n d c s c 胃 a r e w i l l b e n e g a t i v e . h e n c e \sin 胃 = \sqrt{1 - c o s^{2} 胃} = \sqrt{1 - \frac{{(- 1)}^{2}}{3^{2}}} = \sqrt{1 - \frac{1}{9}} = \sqrt{\frac{8}{9}} = \frac{2 \sqrt{2}}{3}$

Step 3.Find the value of secθ and cscθ

$S i n c e \cos 胃 = \frac{- 1}{3}, t h e n s e c 胃 = \frac{1}{\cos 胃} = \frac{1}{\frac{- 1}{3}} = - 3 c s c 胃 = \frac{1}{\sin 胃} = \frac{1}{\frac{2 \sqrt{2}}{3}} = \frac{3}{2 \sqrt{2}}$

Step 4. find the values of tanθ and cotθ

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

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃$
$\cos 胃 = \frac{- 1}{3}, \frac{蟺}{2} < 胃 < 蟺$

Short Answer

Step by step solution

.Given information

Step 2. Finding the value sinθ

Step 3.Find the value of secθ and cscθ

Step 4. find the values of tanθ and cotθ

One App. One Place for Learning.

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃cos胃=-13,蟺2<胃<蟺

Short Answer

Step by step solution

.Given information

Step 2. Finding the value sinθ

Step 3.Find the value of secθ and cscθ

Step 4. find the values of tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Geometry

Applied Mathematics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃$
$\cos 胃 = \frac{- 1}{3}, \frac{蟺}{2} < 胃 < 蟺$