Q. 55 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. 55 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$迟补苍胃 = \frac{3}{4}, 蝉颈苍胃 < 0$

Short Answer

Expert verified

The exact values of trigonometric functions are,

$蝉别肠胃 = - \frac{5}{4} 肠辞蝉胃 = - \frac{4}{5} 蝉颈苍胃 = - \frac{3}{5} 肠辞迟胃 = \frac{4}{3} 肠蝉肠胃 = - \frac{5}{3}$

Step by step solution

Step 1. Given Information

Given trigonometric functions is $迟补苍胃 = \frac{3}{4}, 蝉颈苍胃 < 0 .$ To find the exact values of trigonometric functions using substitution.

Step 2. Solve a equation

It implies that $肠辞蝉胃 < 0$ and angle is III quadrant. On using the equation $\tan^{2} 胃 + 1 = \sec^{2} 胃 \sec^{2} 胃 = 卤 \sqrt{\tan^{2} 胃 + 1}$

Step 3. Substitution to find trigonometric function

On substituting the values,

$蝉别肠胃 = - \sqrt{1 + {(\frac{3}{4})}^{2}} = - \sqrt{1 + \frac{9}{16}} = - \sqrt{\frac{25}{16}} 蝉别肠胃 = - \frac{5}{4} 肠辞蝉胃 = \frac{1}{蝉别肠胃} = \frac{1}{- \frac{5}{4}} 肠辞蝉胃 = - \frac{4}{5}$

Step 4. Substitution for sin, cot and csc functions

On using the equation of $蝉颈苍胃 = 卤 \sqrt{1 - \cos^{2} 胃} 蝉颈苍胃 = - \sqrt{1 - {(- \frac{4}{5})}^{2}} = - \sqrt{1 - \frac{16}{25}} 蝉颈苍胃 = - \frac{3}{5} 肠辞迟胃 = \frac{1}{迟补苍胃} = \frac{1}{\frac{3}{4}} 肠辞迟胃 = \frac{4}{3} 肠蝉肠胃 = \frac{1}{蝉颈苍胃} = \frac{1}{- \frac{3}{5}} 肠蝉肠胃 = - \frac{5}{3}$

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$迟补苍胃 = \frac{3}{4}, 蝉颈苍胃 < 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve a equation

Step 3. Substitution to find trigonometric function

Step 4. Substitution for sin, cot and csc functions

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃.迟补苍胃=34,蝉颈苍胃<0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve a equation

Step 3. Substitution to find trigonometric function

Step 4. Substitution for sin, cot and csc functions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$迟补苍胃 = \frac{3}{4}, 蝉颈苍胃 < 0$