Q 54. 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 54. (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$肠蝉肠胃 = 3, 肠辞迟胃 < 0 .$

Short Answer

Expert verified

The exact values are,

$肠辞蝉胃 = - \frac{2 \sqrt{2}}{3} 迟补苍胃 = - \frac{\sqrt{2}}{4} 肠辞迟胃 = - 2 \sqrt{2} 蝉别肠胃 = - \frac{3 \sqrt{2}}{4}$

Step by step solution

Step 1. Given information

Given that the trigonometric function is $肠蝉肠胃 = 3, 肠辞迟胃 < 0 .$ To find the exact values using substitution.

Step 2. Pythagorean theorem

It implies that $蝉颈苍胃 = \frac{1}{肠蝉肠胃} = \frac{1}{3} .$ Since $肠辞迟胃 < 0, 蝉颈苍胃 = \frac{1}{3} > 0$ which implies that $肠辞蝉胃 < 0 .$ On using the Pythagorean theorem,

$\sin^{2} 胃 + \cos^{2} 胃 = 1 \cos^{2} 胃 = 1 - \sin^{2} 胃肠辞蝉胃 = 卤 \sqrt{1 - \sin^{2} 胃}$

Step 3. Substitution to find the values

On substituting the values in the above equation,

$肠辞蝉胃 = - \sqrt{1 - {(\frac{1}{3})}^{2}} = - \sqrt{1 - \frac{1}{9}} 肠辞蝉胃 = - \frac{2 \sqrt{2}}{3} 迟补苍胃 = \frac{y}{x} = \frac{蝉颈苍胃}{肠辞蝉胃} = \frac{\frac{1}{3}}{- \frac{2 \sqrt{2}}{3}} 迟补苍胃 = - \frac{\sqrt{2}}{4}$

Step 4. Substitution to find the values of cot and sec

The reciprocal of cot is tan. On substituting the values,

$肠辞迟胃 = \frac{1}{迟补苍胃} = \frac{1}{- \frac{\sqrt{2}}{4}} 肠辞迟胃 = - 2 \sqrt{2} 蝉别肠胃 = \frac{1}{肠辞蝉胃} = \frac{1}{- \frac{2 \sqrt{2}}{3}} 蝉别肠胃 = - \frac{3 \sqrt{2}}{4}$

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$肠蝉肠胃 = 3, 肠辞迟胃 < 0 .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Pythagorean theorem

Step 3. Substitution to find the values

Step 4. Substitution to find the values of cot and sec

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃.肠蝉肠胃=3,肠辞迟胃<0.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Pythagorean theorem

Step 3. Substitution to find the values

Step 4. Substitution to find the values of cot and sec

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Statistics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$肠蝉肠胃 = 3, 肠辞迟胃 < 0 .$