Q. 96 The graphs of the given pairs of... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 96 (page 412)

The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.
$y = \sin x y = \frac{1}{2}$

Short Answer

Expert verified

The four points of intersection are

$(\frac{蟺}{6}, \frac{1}{2}), (\frac{5 蟺}{6}, \frac{1}{2}), (\frac{13 蟺}{6}, \frac{1}{2}), (\frac{17 蟺}{6}, \frac{1}{2})$ .

Step by step solution

Step 1. Given Information

We are given two equations $y = \sin x$ and $y = \frac{1}{2}$ .

We need to find any four points of intersection of the two graphs.

We will graph the two equations and then find the first point of intersection and then using the properties of sine function we will find the other three points.

Step 2. Graph the functions

The graph of the two equations is given as

It can be seen that the line and the sinusoidal curve intersect each other at infinitely many points and the first point of intersection is $(\frac{蟺}{6}, \frac{1}{2})$ .

Step 3. Find the other points

The sine function is a cyclic function. So

$\sin x = \sin (蟺 - x) sinx = \sin (2 蟺 + x) sinx = \sin (3 蟺 - x)$

So next intersection points are

$x = 蟺 - \frac{蟺}{6} x = \frac{5 蟺}{6}$

role="math" $x = 2 蟺 + \frac{蟺}{6} x = \frac{13 蟺}{6}$

$x = 3 蟺 - \frac{蟺}{6} x = \frac{17 蟺}{6}$

So the four intersecting points are $(\frac{蟺}{6}, \frac{1}{2}), (\frac{5 蟺}{6}, \frac{1}{2}), (\frac{13 蟺}{6}, \frac{1}{2}), (\frac{17 蟺}{6}, \frac{1}{2})$ .

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91影视

The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.
$y = \sin x y = \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph the functions

Step 3. Find the other points

One App. One Place for Learning.

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91影视

The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.y=sinxy=12

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph the functions

Step 3. Find the other points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Calculus

Logic and Functions

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

The graphs of the given pairs of functions intersect infinitely many times. Find four of these points of intersection.
$y = \sin x y = \frac{1}{2}$