sin(t) %3D 2. %3D

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Topic Video
Question
**Solving Trigonometric Equations in the Interval [0, 2π]**

Instructions:
Solve the following equations in the interval \([0, 2\pi]\). Provide your answer as a multiple of \(\pi\). Do not use decimal numbers. The answer should be a fraction of an integer. Note: \(\pi\) is already included in the answer, so just enter the appropriate multiple.

Example:
If the answer is \(\pi/2\), enter 1/2.

1. \(\sin(t) = \frac{\sqrt{3}}{2}\)

   \(t = \underline{\hspace{2cm}} \pi\)

2. \(\sin(t) = \frac{1}{2}\)

   \(t = \underline{\hspace{2cm}} \pi\)

Use this guide to solve each equation, ensuring clarity and precision in your responses.
Transcribed Image Text:**Solving Trigonometric Equations in the Interval [0, 2π]** Instructions: Solve the following equations in the interval \([0, 2\pi]\). Provide your answer as a multiple of \(\pi\). Do not use decimal numbers. The answer should be a fraction of an integer. Note: \(\pi\) is already included in the answer, so just enter the appropriate multiple. Example: If the answer is \(\pi/2\), enter 1/2. 1. \(\sin(t) = \frac{\sqrt{3}}{2}\) \(t = \underline{\hspace{2cm}} \pi\) 2. \(\sin(t) = \frac{1}{2}\) \(t = \underline{\hspace{2cm}} \pi\) Use this guide to solve each equation, ensuring clarity and precision in your responses.
Expert Solution
Step 1

Solution - Given - Sint = 32We know that -Sinπ3 = 32Hence,Sint = Sinπ3t = sin-1sinπ3                                      Using - sin-1sinθ = θt = π3                                                        

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