Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions

Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo

Blitzer 3rd Edition

Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions

Problema 68

Capitolo 2, Problema 68

In Exercises 67–68, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 4. y = cos πx + sin π/2 x

Guida verificata passo dopo passo

Identify the given function: \(y = \cos(\pi x) + \sin\left(\frac{\pi}{2} x\right)\), which is a sum of two trigonometric functions.

Choose values of \(x\) in the interval \(0 \leq x \leq 4\). For example, select integer values \(x = 0, 1, 2, 3, 4\) to start plotting points.

Calculate the \(y\)-coordinate for each chosen \(x\) by evaluating each trigonometric term separately: compute \(\cos(\pi x)\) and \(\sin\left(\frac{\pi}{2} x\right)\), then add these two results to get \(y\).

Plot each point \((x, y)\) on the coordinate plane using the values found in the previous step.

Connect the plotted points smoothly to graph the function over the interval \(0 \leq x \leq 4\), noting the periodic behavior of the cosine and sine components.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Graphing Trigonometric Functions

Graphing trigonometric functions involves plotting points based on their values at specific x-coordinates. For functions like y = cos(πx) and y = sin(π/2 x), understanding their periodicity and amplitude helps in accurately sketching their curves over the given interval.

Video consigliato:

Percorso guidato

6:04

Introduction to Trigonometric Functions

Sum of Functions (Adding y-coordinates)

When combining functions by adding their y-values, the resulting graph at each x is the sum of the individual function values. This method requires calculating y-values of each function separately at given x-points and then adding them to find the new y-coordinate for the combined function.

Video consigliato:

Percorso guidato

5:20

Example 7

Trigonometric Function Periods and Frequencies

The period of a trigonometric function is the length of one complete cycle. For y = cos(πx), the period is 2, and for y = sin(π/2 x), the period is 4. Knowing these periods helps in determining key points and behavior of the functions within the interval 0 ≤ x ≤ 4.

Video consigliato:

Percorso guidato

5:33

Period of Sine and Cosine Functions

Pratica correlata

Domanda del libro di testo

In Exercises 63–82, use a sketch to find the exact value of each expression. tan [cos⁻¹ (− 1/3)]

853

views

Domanda del libro di testo

In Exercises 63–82, use a sketch to find the exact value of each expression. _ sin (cos⁻¹ √2/2)

975

views

Domanda del libro di testo

In Exercises 75–78, graph one period of each function. y = |2 cos x/2|

558

views

Domanda del libro di testo

In Exercises 63–82, use a sketch to find the exact value of each expression. tan [sin⁻¹ (− 3/5)]

697

views

Domanda del libro di testo

In Exercises 67–68, an object is attached to a coiled spring. In Exercise 67, the object is pulled down (negative direction from the rest position) and then released. In Exercise 68, the object is propelled downward from its rest position. Write an equation for the distance of the object from its rest position after t seconds.

747

views

Domanda del libro di testo

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = cos x + sin 2x

687

views