Q. 47 The exact value of the expressio... [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 7: Q. 47 (page 504)

The exact value of the expression.
$\cos \frac{5 蟺}{12}$

Short Answer

Expert verified

The value of $\cos \frac{5 蟺}{12} = \frac{1}{4} (\sqrt{6} - \sqrt{2})$

Step by step solution

Step 1. Given information

The given expression is $\cos \frac{5 蟺}{4}$

Step 2. Find the values of sinπ12 and cosπ12

We know that,

$\sin (\frac{蟺}{12}) = \sin (\frac{蟺}{3} - \frac{蟺}{4}) \sin (\frac{蟺}{3} - \frac{蟺}{4}) = \sin \frac{蟺}{3} \cos \frac{蟺}{4} - \cos \frac{蟺}{3} \sin \frac{蟺}{4} = \frac{\sqrt{2}}{2} 路 \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2} 路 \frac{1}{2} \sin \frac{蟺}{12} = \frac{\sqrt{6} - \sqrt{2}}{4}$

We know that,

$\cos (\frac{蟺}{3} - \frac{蟺}{4}) = \cos \frac{蟺}{3} \cos \frac{蟺}{4} + \sin \frac{蟺}{3} \sin \frac{蟺}{4} = \frac{\sqrt{2}}{2} \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \frac{1}{2} \cos \frac{蟺}{12} = \frac{\sqrt{6} + \sqrt{2}}{4}$

Step 3. Value of cos5π12

Substituting $\sin \frac{蟺}{12}$ and $\cos \frac{蟺}{12}$ , we get:

role="math" localid="1646592385844" $\cos \frac{5 蟺}{12} = \cos \frac{蟺}{2} \cos \frac{蟺}{12} + \sin \frac{蟺}{2} \sin \frac{蟺}{12} \cos \frac{5 蟺}{12} = 0 路 (\frac{\sqrt{6} + \sqrt{2}}{4}) + (1) (\frac{\sqrt{6} - \sqrt{2}}{4}) \cos \frac{5 蟺}{12} = \frac{1}{4} (\sqrt{6} - \sqrt{2})$

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91影视

The exact value of the expression.
$\cos \frac{5 蟺}{12}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the values of sinπ12 and cosπ12

Step 3. Value of cos5π12

One App. One Place for Learning.

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91影视

The exact value of the expression.cos5蟺12

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the values of sinπ12 and cosπ12

Step 3. Value of cos5π12

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Probability and Statistics

Logic and Functions

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

The exact value of the expression.
$\cos \frac{5 蟺}{12}$