Q.46 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.46 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃$
$\sin 胃 = - \frac{5}{13}, w h e r e 胃 l i e s o n 3 r d q u a d r a n t .$

Short Answer

Expert verified

The exact values are $\cos 胃 = \frac{- 12}{13}, c s c 胃 = - \frac{13}{5}, s e c 胃 = - \frac{13}{12}, \tan 胃 = \frac{5}{12}, c o t 胃 = \frac{12}{5}$

Step by step solution

Step 1. Given information

Here $\sin 胃 = - \frac{5}{13} w h e r e 胃 l i e s o n 3 r d q u a d r a n t$

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

. description of finding the value of cosθ

Here $\sin 胃 = - \frac{5}{13} W e k n o w t h a t \sin^{2} 胃 + \cos^{2} 胃 = 1 \cos 胃 = 卤 \sqrt{1 - \sin^{2} 胃} a n d \sin c e \sin 胃 i s o n t h i r d q u a d r a n t a l l o t h e r e x c e p t \tan 胃 a n d c o t 胃 a r e w i l l b e n e g a t i v e . h e n c e \cos 胃 = - \sqrt{1 - \sin^{2} 胃} = - \sqrt{1 - \frac{{(- 5)}^{2}}{13^{2}}} = - \sqrt{1 - \frac{25}{169}} = - \frac{12}{13}$

Step 3. Finding the values of cscθ and secθ

in this question

$\cos 胃 = - \frac{12}{13}, t h e n s e c 胃 = \frac{1}{\cos 胃} = \frac{1}{- \frac{12}{13}} = - \frac{13}{12} c s c 胃 = \frac{1}{\sin 胃} = \frac{1}{- \frac{5}{13}} = - \frac{13}{5}$

Step 4. Finding the values of tan θ, cotθ

Since

$\sin 胃 = - \frac{5}{13} a n d \cos 胃 = - \frac{12}{13} \tan 胃 = \frac{\sin 胃}{\cos 胃} = \frac{- \frac{5}{13}}{- \frac{12}{13}} = \frac{5}{12} c o t 胃 = \frac{1}{\tan 胃} = \frac{1}{\frac{5}{12}} = \frac{12}{5}$

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃$
$\sin 胃 = - \frac{5}{13}, w h e r e 胃 l i e s o n 3 r d q u a d r a n t .$

Short Answer

Step by step solution

Step 1. Given information

. description of finding the value of cosθ

Step 3. Finding the values of cscθ and secθ

Step 4. Finding the values of tan θ, cotθ

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Most popular questions from this chapter

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃sin胃=-513,where胃lieson3rdquadrant.

Short Answer

Step by step solution

Step 1. Given information

. description of finding the value of cosθ

Step 3. Finding the values of cscθ and secθ

Step 4. Finding the values of tan θ, cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Geometry

Pure Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃$
$\sin 胃 = - \frac{5}{13}, w h e r e 胃 l i e s o n 3 r d q u a d r a n t .$