Q.44 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.44 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$\cos 胃 = \frac{3}{5}, 胃 i s o n f o u r t h q u a d r a n t$

Short Answer

Expert verified

The value of $\sin 胃 = - \frac{4}{5}, s e c 胃 = \frac{5}{3}, c s c 胃 = - \frac{5}{4}, \tan 胃 = - \frac{4}{3} a n d c o t 胃 = - \frac{3}{4}$

Step by step solution

Step 1. Given information

Here $\cos 胃 = \frac{3}{5}, 胃 i s o n f o u r t h q u a d r a n t i s g i v e n .$

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

Step 2.Description of finding the value of sinθ

In this question $\cos 胃 = \frac{3}{5} W e k n o w t h a t \sin^{2} 胃 + \cos^{2} 胃 = 1 \sin 胃 = 卤 \sqrt{1 - \cos^{2} 胃} a n d \sin c e \cos 胃 i s o n f o u r t h q u a d r a n t a l l o t h e r t r i g n o m e t r i c r a t i o s w i l l b e n e g a t i v e . h e n c e \sin 胃 = - \sqrt{1 - \cos^{2} 胃} = - \sqrt{1 - \frac{3^{2}}{5^{2}}} = - \sqrt{1 - \frac{9}{25}} = - \frac{4}{5}$

Step 3 . Finding the value of cscθ and secθ

According to the question

$\cos 胃 = \frac{3}{5} t h e n s e c 胃 = \frac{1}{\cos 胃} = \frac{1}{\frac{3}{5}} = \frac{5}{3} c s c 胃 = \frac{1}{\sin 胃} = \frac{1}{- \frac{4}{5}} = - \frac{5}{4}$

Step 4. Finding the value of tanθ and cot θ

Since $\sin 胃 = - \frac{4}{5} a n d \cos 胃 = \frac{3}{5} \tan 胃 = \frac{\sin 胃}{\cos 胃} = \frac{- \frac{4}{5}}{\frac{3}{5}} = \frac{- 4}{3} c o t 胃 = \frac{1}{\tan 胃} = \frac{1}{- \frac{4}{3}} = - \frac{3}{4}$

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$\cos 胃 = \frac{3}{5}, 胃 i s o n f o u r t h q u a d r a n t$

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value of sinθ

Step 3 . Finding the value of cscθ and secθ

Step 4. Finding the value of tanθ and cot θ

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃.cos胃=35,胃isonfourthquadrant

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value of sinθ

Step 3 . Finding the value of cscθ and secθ

Step 4. Finding the value of tanθ and cot θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Statistics

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Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$\cos 胃 = \frac{3}{5}, 胃 i s o n f o u r t h q u a d r a n t$