(표) + sin (포). Give the exact value of COS O1 V3 V2 O 1+v3
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![### Problem Statement
**Question:**
Give the exact value of \( \cos\left(\frac{\pi}{4}\right) + \sin\left(\frac{\pi}{4}\right) \).
**Answer Choices:**
1. \( \quad 1 \)
2. \( \quad \frac{\sqrt{2}}{2} \)
3. \( \quad \sqrt{3} \)
4. \( \quad \sqrt{2} \)
5. \( \quad \frac{1 + \sqrt{3}}{2} \)
**Explanation:**
To solve the given trigonometric problem, we need to recall the exact values of the cosine and sine functions for the angle \( \frac{\pi}{4} \).
1. The value of \( \cos\left(\frac{\pi}{4}\right) \) is \( \frac{\sqrt{2}}{2} \).
2. The value of \( \sin\left(\frac{\pi}{4}\right) \) is \( \frac{\sqrt{2}}{2} \).
Adding these values together:
\[ \cos\left(\frac{\pi}{4}\right) + \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} = \frac{2\sqrt{2}}{2} = \sqrt{2} \]
Therefore, the correct answer is:
\[ \boxed{\sqrt{2}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2Fe27b82e7-1f37-4336-a03e-1aa2d942d6c8%2Farjdr5d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Question:**
Give the exact value of \( \cos\left(\frac{\pi}{4}\right) + \sin\left(\frac{\pi}{4}\right) \).
**Answer Choices:**
1. \( \quad 1 \)
2. \( \quad \frac{\sqrt{2}}{2} \)
3. \( \quad \sqrt{3} \)
4. \( \quad \sqrt{2} \)
5. \( \quad \frac{1 + \sqrt{3}}{2} \)
**Explanation:**
To solve the given trigonometric problem, we need to recall the exact values of the cosine and sine functions for the angle \( \frac{\pi}{4} \).
1. The value of \( \cos\left(\frac{\pi}{4}\right) \) is \( \frac{\sqrt{2}}{2} \).
2. The value of \( \sin\left(\frac{\pi}{4}\right) \) is \( \frac{\sqrt{2}}{2} \).
Adding these values together:
\[ \cos\left(\frac{\pi}{4}\right) + \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} = \frac{2\sqrt{2}}{2} = \sqrt{2} \]
Therefore, the correct answer is:
\[ \boxed{\sqrt{2}} \]
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