/*! 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 7 Find the period and amplitude. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 7

Find the period and amplitude. $$y=\frac{3}{4} \cos \frac{x}{2}$$

Short Answer

Expert verified
The amplitude of the given function is \(\frac{3}{4}\) and the period is \(4\pi\)

Step by step solution

01

Identify the Amplitude

The amplitude (A) of the function can be identified as the absolute value of the coefficient of the cosine function. In the given function \(y=\frac{3}{4} \cos \frac{x}{2}\), the coefficient of the cosine function is \(\frac{3}{4}\) which also happens to be the amplitude.
02

Identify the Period

The period (T) of a function can be calculated as \(T=\frac{2\pi}{|B|}\), where B is the coefficient of x in the trigonometric function. In the given function \(y=\frac{3}{4} \cos \frac{x}{2}\), the coefficient of x is \(\frac{1}{2}\). Substituting to the formula we get \(T=\frac{2\pi}{|\frac{1}{2}|} = 4\pi\).
03

Wrap-up

By identifying the coefficients of the given trigonometric function \(y=\frac{3}{4} \cos \frac{x}{2}\), it was determined that the amplitude of the function is \(\frac{3}{4}\) and the period of the function is \(4\pi\).

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

Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$f(x)=e^{-x} \cos x$$

Prove that the area of a circular sector of radius \(r\) with central angle \(\theta\) is \(A=\frac{1}{2} \theta r^{2}\) where \(\theta\) is measured in radians.

Define the inverse cotangent function by restricting the domain of the cotangent function to the interval \((0, \pi),\) and sketch the graph of the inverse trigonometric function.

Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\cos ^{2} \frac{\pi x}{2}, \quad g(x)=\frac{1}{2}(1+\cos \pi x)$$

Converting to \(\mathrm{D}^{\circ} \mathrm{M}^{\prime} \mathrm{S}^{\prime \prime}\) Form \(\quad\) Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(240.6^{\circ}\) (b) \(-145.8^{\circ}\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

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.