Q.43 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.43 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃 .$
localid="1646686875779" $\sin 胃 = \frac{12}{13}, 胃 i n s e c o n d q u a d r a n t .$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

Here $\sin 胃 = \frac{12}{13}, 胃 i n s e c o n d q u a d r a n t .$ is given.

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

. Description of finding the value of cos θ

According to the question $\sin 胃 = \frac{12}{13} w h e r e 胃 l i e s o n 2 n d q u a d r a n t . W e k n o w t h a t \sin^{2} 胃 + \cos^{2} 胃 = 1 \cos 胃 = 卤 \sqrt{1 - \sin^{2} 胃} a n d \sin c e \sin 胃 i s o n 2 n d q u a d r a n t a l l o t h e r t r i g n o m e t r i c r a t i o s w i l l b e n e g a t i v e . h e n c e \cos 胃 = - \sqrt{1 - \sin^{2} 胃} = - \sqrt{1 - \frac{12^{2}}{13^{2}}} = - \sqrt{1 - \frac{144}{169}} = - \sqrt{\frac{25}{169}} = - \frac{5}{13}$

Step 3. Describing about find the values of cscθ,secθ

Here

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

Step 4.Describing about find the values of tanθ and cotθ

We know that

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

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃 .$
localid="1646686875779" $\sin 胃 = \frac{12}{13}, 胃 i n s e c o n d q u a d r a n t .$

Short Answer

Step by step solution

Step 1. Given information

. Description of finding the value of cos θ

Step 3. Describing about find the values of cscθ,secθ

Step 4.Describing about find the values of tanθ and cotθ

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃.localid="1646686875779" sin胃=1213,胃insecondquadrant.

Short Answer

Step by step solution

Step 1. Given information

. Description of finding the value of cos θ

Step 3. Describing about find the values of cscθ,secθ

Step 4.Describing about find the values of tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Mechanics Maths

Geometry

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃 .$
localid="1646686875779" $\sin 胃 = \frac{12}{13}, 胃 i n s e c o n d q u a d r a n t .$