/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 99 Determine the amplitude and peri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 99

Determine the amplitude and period of \(y=3 \sin \frac{1}{2} x\) Then graph the function for \(0 \leq x \leq 4 \pi\)

Short Answer

Expert verified
The amplitude of the function \(y=3 \sin \frac{1}{2} x\) is 3, and the period is \(4\pi\).

Step by step solution

01

Determine the Amplitude

The amplitude of a sine function is given by the absolute value of the coefficient of the sine term. In this case, it is |3| = 3.
02

Determine the Period

The period of a trigonometric function is given by the formula \(2\pi / |B|\), where B is the coefficient of x in the sine function. Here, \(B = \frac{1}{2}\). So the period of the function is \(2\pi / \frac{1}{2} = 4\pi\).
03

Graph the Function

Plot the function \(y = 3 \sin \frac{1}{2} x\), which has the amplitude as 3 and period as \(4\pi\), for the interval \(0 \leq x \leq 4 \pi\). Also plot several points for each quarter period.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

solve each equation on the interval \([0,2 \pi) .\) \(2 \cos ^{3} x+\cos ^{2} x-2 \cos x-1=0\) (Hint: Use factoring by grouping.)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. After using an identity to determine the exact value of \(\sin 105^{\circ},\) I verified the result with a calculator.

Solve: \(\log x+\log (x+1)=\log 12\) (Section \(4.4,\) Example 8 )

Use a graphing utility to approximate the solutions of each equation in the interval \([0,2 \pi) .\) Round to the nearest hundredth of a radian. $$ \sin 2 x=2-x^{2} $$

Use words to describe the formula for each of the following: the sine of the sum of two angles.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.