↓ G 235ed6fuatе/work .schoolspip.com 15433/items/ ㅠ ㅠ √2 1. Solve the problem. Use sin 1 and sin 2 4 2 ㅠ Given x = -. Use the formula cos²x = 1 - sin² x to find cos 2 2
↓ G 235ed6fuatе/work .schoolspip.com 15433/items/ ㅠ ㅠ √2 1. Solve the problem. Use sin 1 and sin 2 4 2 ㅠ Given x = -. Use the formula cos²x = 1 - sin² x to find cos 2 2
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Solving Trigonometric Problems Using Pythagorean Identities
#### Problem 1
**Objective:**
Solve the problem using the given trigonometric values and identities.
**Given Trigonometric Values:**
1. \(\sin \frac{\pi}{2} = 1\)
2. \(\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}\)
**Problem Statement:**
Given \(x = \frac{\pi}{2}\), use the following trigonometric identity to find \(\cos \frac{\pi}{2}\):
\[ \cos^2 x = 1 - \sin^2 x \]
**Solution:**
1. Substitute \(x = \frac{\pi}{2}\) into the identity:
\[ \cos^2 \frac{\pi}{2} = 1 - \sin^2 \frac{\pi}{2} \]
2. Use the given value \(\sin \frac{\pi}{2} = 1\):
\[ \cos^2 \frac{\pi}{2} = 1 - 1^2 \]
\[ \cos^2 \frac{\pi}{2} = 1 - 1 \]
\[ \cos^2 \frac{\pi}{2} = 0 \]
3. Taking the square root of both sides, we get:
\[ \cos \frac{\pi}{2} = 0 \]
Thus, \(\cos \frac{\pi}{2} = 0\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38eccb3c-f53a-4e25-8f36-f53b6ab0f887%2F75733956-08fe-464c-8267-e9910f044787%2Fw7b7xiw_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving Trigonometric Problems Using Pythagorean Identities
#### Problem 1
**Objective:**
Solve the problem using the given trigonometric values and identities.
**Given Trigonometric Values:**
1. \(\sin \frac{\pi}{2} = 1\)
2. \(\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}\)
**Problem Statement:**
Given \(x = \frac{\pi}{2}\), use the following trigonometric identity to find \(\cos \frac{\pi}{2}\):
\[ \cos^2 x = 1 - \sin^2 x \]
**Solution:**
1. Substitute \(x = \frac{\pi}{2}\) into the identity:
\[ \cos^2 \frac{\pi}{2} = 1 - \sin^2 \frac{\pi}{2} \]
2. Use the given value \(\sin \frac{\pi}{2} = 1\):
\[ \cos^2 \frac{\pi}{2} = 1 - 1^2 \]
\[ \cos^2 \frac{\pi}{2} = 1 - 1 \]
\[ \cos^2 \frac{\pi}{2} = 0 \]
3. Taking the square root of both sides, we get:
\[ \cos \frac{\pi}{2} = 0 \]
Thus, \(\cos \frac{\pi}{2} = 0\).
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