Q. 53 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. 53 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$蝉别肠胃 = 2, 蝉颈苍胃 < 0 .$

Short Answer

Expert verified

The exact values of the trigonometric functions are,

$蝉颈苍胃 = - \frac{\sqrt{3}}{2} 迟补苍胃 = - \sqrt{3} 肠辞迟胃 = - \frac{\sqrt{3}}{3} 肠蝉肠胃 = - \frac{2 \sqrt{3}}{3}$

Step by step solution

Step 1. Given Information

Given that the function is $蝉别肠胃 = 2, 蝉颈苍胃 < 0 .$ To find the exact values using substitution.

Step 2. Phythagorean identity

It implies that $肠辞蝉胃 = \frac{1}{蝉别肠胃} = \frac{1}{2}$ . Since $蝉颈苍胃 < 0, 肠辞蝉胃 = \frac{1}{2} > 0 .$ On using Phythagorean identity as $\sin^{2} 胃 + \cos^{2} 胃 = 1$ . On using this equation to solve for $蝉颈苍胃,$

$\sin^{2} 胃 + \cos^{2} 胃 = 1 蝉颈苍胃 = 卤 \sqrt{1 - \cos^{2} 胃}$

On substituting the values,

$蝉颈苍胃 = - \sqrt{1 - {(\frac{1}{2})}^{2}} = - \sqrt{1 - \frac{1}{4}} = - \sqrt{\frac{3}{4}} 蝉颈苍胃 = - \frac{\sqrt{3}}{2}$

Step 3. Definition of unit circle

The definition of unit circle is $蝉颈苍胃 = y, 肠辞蝉胃 = x .$

$迟补苍胃 = \frac{y}{x} 迟补苍胃 = \frac{蝉颈苍胃}{肠辞蝉胃} = \frac{- \frac{\sqrt{3}}{2}}{\frac{1}{2}} 迟补苍胃 = - \sqrt{3} 肠辞迟胃 = \frac{1}{迟补苍胃} = \frac{1}{- \sqrt{3}} 肠辞迟胃 = - \frac{\sqrt{3}}{2} 肠蝉肠胃 = \frac{1}{蝉颈苍胃} = - \frac{\frac{1}{\sqrt{3}}}{2} = - \frac{2}{\sqrt{3}} 肠蝉肠胃 = - \frac{2 \sqrt{3}}{3}$

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$蝉别肠胃 = 2, 蝉颈苍胃 < 0 .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Phythagorean identity

Step 3. Definition of unit circle

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃.蝉别肠胃=2,蝉颈苍胃<0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Phythagorean identity

Step 3. Definition of unit circle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$蝉别肠胃 = 2, 蝉颈苍胃 < 0 .$