Q. 51 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. 51 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃 .$
role="math" localid="1646521470980" $蝉颈苍胃 = \frac{2}{3}, 迟补苍胃 < 0$

Short Answer

Expert verified

The exact values are,

$肠辞蝉胃 = - \frac{\sqrt{5}}{3} 迟补苍胃 = - \frac{2 \sqrt{5}}{5} 肠蝉肠胃 = \frac{3}{2} 蝉别肠胃 = - \frac{3 \sqrt{5}}{5} 肠辞迟胃 = - \frac{\sqrt{5}}{2}$

Step by step solution

Step 1. Given Information

Given that the function is $蝉颈苍胃 = \frac{2}{3}, 迟补苍胃 < 0 .$ To find the exact values of $胃$ .

Step 2. Using theorem and signs

There is a difference in sign due to the quadrant of II or IV. When $y = 2 > 0,$ the quadrant is in II. The angle lies to the point $P = (x, y)$ in the standard position. The radius of the circle has $r^{2} = x^{2} + y^{2} .$ The values are $蝉颈苍胃 = \frac{y}{r}, y = 2, r = 3 .$ On solving and substituting,

$x^{2} = r^{2} - y^{2} x^{2} = {(3)}^{2} - {(2)}^{2} x^{2} = 9 - 4 x^{2} = 5 x = - \sqrt{5}$

Substitution to find exact values

On substituting the values for exact values are,

$肠辞蝉胃 = \frac{x}{r} 肠辞蝉胃 = - \frac{\sqrt{5}}{3} 迟补苍胃 = \frac{y}{x} 迟补苍胃 = - \frac{2}{\sqrt{5}} . \frac{\sqrt{5}}{\sqrt{5}} 迟补苍胃 = - \frac{2 \sqrt{5}}{5}$

Substitution to find exact values

On finding the exact values are,

$肠蝉肠胃 = \frac{r}{y} 肠蝉肠胃 = \frac{3}{2} 蝉别肠胃 = \frac{r}{x} 蝉别肠胃 = - \frac{3}{\sqrt{5}} . \frac{\sqrt{5}}{\sqrt{5}} 蝉别肠胃 = - \frac{3 \sqrt{5}}{5} 肠辞迟胃 = \frac{x}{y} 肠辞迟胃 = - \frac{\sqrt{5}}{2}$

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃 .$
role="math" localid="1646521470980" $蝉颈苍胃 = \frac{2}{3}, 迟补苍胃 < 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Using theorem and signs

Substitution to find exact values

Substitution to find exact values

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃.role="math" localid="1646521470980" 蝉颈苍胃=23,迟补苍胃<0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Using theorem and signs

Substitution to find exact values

Substitution to find exact values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Decision Maths

Mechanics Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃 .$
role="math" localid="1646521470980" $蝉颈苍胃 = \frac{2}{3}, 迟补苍胃 < 0$