Find the smallest positive value of t. sin(2#t) = 4
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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Question
![**Problem Statement:**
Find the smallest positive value of \( t \).
\[
\sin(2\pi t) = \frac{\sqrt{3}}{2}
\]
\( t = \) [Input box]
**Additional Resources:**
- **Need Help?**
- [Read It]
- [Talk to a Tutor]
**Understanding the Problem:**
This problem requires you to find the smallest positive value of \( t \) for which the equation \(\sin(2\pi t) = \frac{\sqrt{3}}{2}\) holds true.
**Key Concepts:**
- The sine function, \(\sin(x)\), returns the y-coordinate of a point on the unit circle corresponding to the angle \( x \) measured in radians.
- The value \(\frac{\sqrt{3}}{2}\) is a common sine value in trigonometry, often corresponding to specific standard angles (e.g., \(\frac{\pi}{3}\) or \(60^\circ\)).
**Solution Approach:**
- Determine at which angle the sine function value is \(\frac{\sqrt{3}}{2}\).
- Adjust the angle to find the smallest positive value of \( t \).
**Interactive Elements:**
Use the "Read It" and "Talk to a Tutor" buttons for detailed explanation and personalized assistance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe069bb76-d12a-4659-9fff-a2d2132df1d6%2Fd8bcf168-61f8-4c90-a35e-3208ebdf7eab%2Fr7cz60s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the smallest positive value of \( t \).
\[
\sin(2\pi t) = \frac{\sqrt{3}}{2}
\]
\( t = \) [Input box]
**Additional Resources:**
- **Need Help?**
- [Read It]
- [Talk to a Tutor]
**Understanding the Problem:**
This problem requires you to find the smallest positive value of \( t \) for which the equation \(\sin(2\pi t) = \frac{\sqrt{3}}{2}\) holds true.
**Key Concepts:**
- The sine function, \(\sin(x)\), returns the y-coordinate of a point on the unit circle corresponding to the angle \( x \) measured in radians.
- The value \(\frac{\sqrt{3}}{2}\) is a common sine value in trigonometry, often corresponding to specific standard angles (e.g., \(\frac{\pi}{3}\) or \(60^\circ\)).
**Solution Approach:**
- Determine at which angle the sine function value is \(\frac{\sqrt{3}}{2}\).
- Adjust the angle to find the smallest positive value of \( t \).
**Interactive Elements:**
Use the "Read It" and "Talk to a Tutor" buttons for detailed explanation and personalized assistance.
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