Q.47 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.47 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃$ .
$\sin 胃 = \frac{5}{13}, 90^{o} < 胃 < 180^{o}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

Here $\sin 胃 = \frac{5}{13}, 90^{o} < 胃 < 180^{o}$ are given.

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

Step 2.Description of finding the value cosθ.

In this question $\sin 胃 = \frac{5}{13} W e k n o w t h a t \sin^{2} 胃 + \cos^{2} 胃 = 1 \cos 胃 = 卤 \sqrt{1 - \sin^{2} 胃}, h e r e 胃 l i e s o n 90^{o} < 胃 < 180^{o} s o \sin 胃 i s o n s e c o n d q u a d r a n t a l l o t h e r e x c e p t \sin 胃 a n d c s c 胃 a r e w i l l b e n e g a t i v e . h e n c e \cos 胃 = - \sqrt{1 - \sin^{2} 胃} = - \sqrt{1 - \frac{5^{2}}{13^{2}}} = - \sqrt{1 - \frac{25}{169}} = - \frac{12}{13}$

Step 3. finding the value of secθ and cscθ

Here

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

Step 4. Finding the value for tanθ and cotθ

We know that

\tan 胃 = \frac{\sin 胃}{\cos 胃}, \sin 胃 = \frac{5}{13} a n d \cos 胃 = - \frac{12}{13} = \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 $胃$ .
$\sin 胃 = \frac{5}{13}, 90^{o} < 胃 < 180^{o}$

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value cosθ.

Step 3. finding the value of secθ and cscθ

Step 4. Finding the value for 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.sin胃=513,90o<胃<180o

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value cosθ.

Step 3. finding the value of secθ and cscθ

Step 4. Finding the value for tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Statistics

Decision Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃$ .
$\sin 胃 = \frac{5}{13}, 90^{o} < 胃 < 180^{o}$