/*! 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 51 Sketch the graph of the function... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 51

Sketch the graph of the function. (Include two full periods.) $$y=\sin \left(x-\frac{\pi}{2}\right)$$

Short Answer

Expert verified
The graph of the function \(y=\sin(x-\frac{\pi}{2})\) represents a rightward shift of the sine function by \(\frac{\pi}{2}\) units, oscillating between -1 and 1 and maintaining a period of \(2\pi\).

Step by step solution

01

Understanding the base function

Begin by recalling the standard sine function \(y=\sin x\), which has a period of \(2\pi\) and which oscillates between -1 and 1.
02

Understanding the transformation

The function \(y=\sin \left(x-\frac{\pi}{2}\right)\) is a horizontal shift of the standard sine function. It is shifted \(\frac{\pi}{2}\) units to right. This does not affect the period or the amplitude of the function.
03

Plotting the function

Now, to sketch two full periods of the function \(\sin(x - \frac{\pi}{2})\), it can be helpful to first plot the sine function \(y=\sin x\), then shift all points to the right by \(\frac{\pi}{2}\). Start at the point (0, 0), but remember to shift to the right by \(\frac{\pi}{2}\), so the first point becomes \((\frac{\pi}{2}, 0)\). Follow this procedure by marking equivalent points of the sine curve, and shift them by \(\frac{\pi}{2}\). Ensure to complete two full periods.

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

Finding the Central Angle Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an are of length \(s\). \(r=14\) feet \(, s=8\) feet

Sketch a graph of the function. $$f(x)=\arccos \frac{x}{4}$$

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) \(-145.8^{\circ}\)

Sketch a graph of the function. $$g(t)=\arccos (t+2)$$

A car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet. (a) Find the number of revolutions per minute the wheels are rotating. (b) Find the angular speed of the wheels in radians per minute.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.