Q.48 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.48 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃$
$\cos 胃 = \frac{4}{5}, 270^{o} < 胃 < 360^{o}$

Short Answer

Expert verified

The exact values are

$\sin 胃 = - \frac{3}{5}, s e c 胃 = \frac{5}{4}, c s c 胃 = - \frac{5}{3}, \tan 胃 = - \frac{3}{4}, c o t 胃 = - \frac{4}{3}$

Step by step solution

Step 1. Given information

$\cos 胃 = \frac{4}{5}, 270^{0} < 胃 < 360^{0}$ is given.

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

Step 2. Find the value of sinθ

$W e k n o w t h a t \sin^{2} 胃 + \cos^{2} 胃 = 1, h e r e \cos 胃 = \frac{4}{5} \sin 胃 = 卤 \sqrt{1 - \cos^{2} 胃}, h e r e 胃 l i e s o n 270^{o} < 胃 < 360^{o} s o \cos 胃 i s o n f o u r t h q u a d r a n t a l l o t h e r e x c e p t \cos 胃 a n d s e c 胃 a r e w i l l b e n e g a t i v e . h e n c e \sin 胃 = - \sqrt{1 - c o s^{2} 胃} = - \sqrt{1 - \frac{4^{2}}{5^{2}}} = - \sqrt{1 - \frac{16}{25}} = - \frac{3}{5}$

step 3. Find the values of secθ, cscθ

According to the question

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

Step 4. Find the values of tanθ and cotθ

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

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃$
$\cos 胃 = \frac{4}{5}, 270^{o} < 胃 < 360^{o}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value of sinθ

step 3. Find the values of secθ, 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=45,270o<胃<360o

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value of sinθ

step 3. Find the values of secθ, 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

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃$
$\cos 胃 = \frac{4}{5}, 270^{o} < 胃 < 360^{o}$