Q. 21 In problem 11-22,find the exact ... [FREE SOLUTION]

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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 21 (page 485)

In problem 11-22,find the exact value of the each expression $s e c (\frac{- 蟺}{12})$
$s e c (- \frac{蟺}{12})$

Short Answer

Expert verified

The exact value of $s e c (\frac{- 蟺}{12}) = \frac{4}{\sqrt{6} + \sqrt{2}}$ $s e c (\frac{- 蟺}{12}) = \frac{4}{\sqrt{6} + \sqrt{2}}$

Step by step solution

Step 1.Given information

The given expression $s e c (- \frac{蟺}{12})$

Step 2.Finding the value of sec-π12

Using the identity $s e c 胃 = \frac{1}{\cos 胃}$ substitute $\frac{1}{\cos (\frac{- 蟺}{12})}$ for $s e c (\frac{- 蟺}{12})$ in the expression.

$s e c (- \frac{蟺}{12}) = \frac{1}{\cos (\frac{- 蟺}{12})}$

Since $(\frac{- 蟺}{12})$ is equal to $\frac{2 蟺}{12} - \frac{3 蟺}{12}, \frac{1}{\cos (\frac{- 蟺}{12})}$ can be written as $\frac{1}{\cos (\frac{2 蟺}{12} - \frac{3 蟺}{12})} o r \frac{1}{\cos (\frac{蟺}{6} - \frac{蟺}{4})}$

Use the difference formula $\cos (伪 - 尾) = \cos 伪 \cos 尾 + \sin 伪 \sin 尾$ to rewrite the expression.

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

Substitute the values for the sine and cosine functions and evaluate the expression.

role="math" localid="1646496121185" $\frac{1}{c o s \frac{蟺}{6} \cos \frac{蟺}{4} + \sin \frac{蟺}{6} \sin \frac{蟺}{4}} = \frac{1}{\frac{\sqrt{3}}{2} . \frac{\sqrt{2}}{2} + \frac{1}{2} . \frac{\sqrt{2}}{2}} = \frac{1}{\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}} = \frac{1}{\frac{1}{4} (\sqrt{6} + \sqrt{2})} = \frac{4}{\sqrt{6} + \sqrt{2}}$

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91影视

In problem 11-22,find the exact value of the each expression $s e c (\frac{- 蟺}{12})$
$s e c (- \frac{蟺}{12})$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Finding the value of sec-π12

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91影视

In problem 11-22,find the exact value of the each expressionsec-蟺12sec-蟺12

Short Answer

Step by step solution

Step 1.Given information

Step 2.Finding the value of sec-π12

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

In problem 11-22,find the exact value of the each expression $s e c (\frac{- 蟺}{12})$
$s e c (- \frac{蟺}{12})$