Q.52 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.52 (page 395)

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$肠辞蝉胃 = - \frac{1}{4}, 迟补苍胃 > 0 .$

Short Answer

Expert verified

The exact values are,

$蝉颈苍胃 = - \frac{\sqrt{15}}{4} 肠蝉肠胃 = - \frac{4 \sqrt{15}}{15} 蝉别肠胃 = - 4 肠辞迟胃 = \frac{\sqrt{15}}{15}$

Step by step solution

Step 1. Given Information

Given that $肠辞蝉胃 = - \frac{1}{4}, 迟补苍胃 > 0$ . To find the exact values for trigonometric functions of angle.

Step 2. Radius of the circle

The angle corresponds to the point $P = (x, y)$ where terminal point is circle. The circle's radius is $r^{2} = x^{2} + y^{2} .$ The values are $肠辞蝉胃 = \frac{x}{r}, x = - 1, r = 4 .$ The tan functions have sine and cosine which occurs in the III and I quadrant. Mainly, $x = - 1 < 0$ must in III quadrant. On solving the value of y,

$y^{2} = r^{2} - x^{2} y^{2} = {(4)}^{2} - {(- 1)}^{2} = 16 - 1 y^{2} = 15 y = \sqrt{15} y = - \sqrt{15}$

Step 3. Finding the exact values

To find the exact values are,

$蝉颈苍胃 = \frac{y}{r} 蝉颈苍胃 = - \frac{\sqrt{15}}{4} y^{2} = r^{2} - x^{2} = {(4)}^{2} - {(- 1)}^{2} y^{2} = 15 y = \sqrt{15} in third quadrant, y = - \sqrt{15}$

Step 4. Substitution

On substituting the values to get the exact values,

$肠蝉肠胃 = \frac{r}{y} = - \frac{4}{\sqrt{15}} . \frac{\sqrt{15}}{\sqrt{15}} 肠蝉肠胃 = - \frac{4 \sqrt{15}}{15} 蝉别肠胃 = \frac{r}{x} = - \frac{4}{1} 蝉别肠胃 = - 4 肠辞迟胃 = \frac{x}{y} = \frac{1}{\sqrt{15}} . \frac{\sqrt{15}}{\sqrt{15}} 肠辞迟胃 = \frac{\sqrt{15}}{15}$

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91影视

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$肠辞蝉胃 = - \frac{1}{4}, 迟补苍胃 > 0 .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Radius of the circle

Step 3. Finding the exact values

Step 4. Substitution

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91影视

Find the exact value of each of the remaining trigonometric functions of 胃.肠辞蝉胃=-14,迟补苍胃>0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Radius of the circle

Step 3. Finding the exact values

Step 4. Substitution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Decision Maths

Pure Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $胃 .$
$肠辞蝉胃 = - \frac{1}{4}, 迟补苍胃 > 0 .$