Chapter 6: Q. 23 (page 395)

In problems 11-26,use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.
$\sec (\frac{7 π}{4})$

Short Answer

Expert verified

The exact value is $\sqrt{2}$ .

Step by step solution

Step 1. Given information.

We have:

$\sec (\frac{7 π}{4})$

Step 2. Find the exact value of trigonometric function.

The function $\sec (\frac{7 π}{4})$ .

$\sec (\frac{7 π}{4}) = \frac{1}{\cos (\frac{7 π}{4})}$

Formula used:

$\cos (x) = \sin (\frac{π}{2} - x)$

$= \frac{1}{\sin (\frac{π}{2} - \frac{7 π}{4})} = \frac{1}{\sin (- \frac{5 π}{4})} = - \frac{1}{\sin (\frac{5 π}{4})} = - \frac{1}{- \frac{\sqrt{2}}{2}} = \sqrt{2}$

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In problems 11-26,use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.
$\sec (\frac{7 π}{4})$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the exact value of trigonometric function.

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In problems 11-26,use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.sec7π4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the exact value of trigonometric function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Decision Maths

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In problems 11-26,use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.
$\sec (\frac{7 π}{4})$