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

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

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 $(\frac{π}{6}, \frac{1}{2})$ .

Step 3. Find the other points

The sine function is a cyclic function. So

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

So next intersection points are

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

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

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

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

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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

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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

Theoretical and Mathematical Physics

Statistics

Logic and Functions

Pure Maths

Probability and Statistics

Geometry

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.
$y = \sin x y = \frac{1}{2}$