Question

Provide a justification as to why no further points of intersection (and therefore solutions) exist in Figure 30 for $x<-\mathrm{\pi }$or $x>4\mathrm{\pi }$.

Short answer

The given equation has no further points of intersection because both lines only cut on the given intersection point.

Step-by-step solution

Step 1. Given Information

Provide a justification as to why no further points of intersection (and therefore solutions) exist in Figure 30 for $x<-\mathrm{\pi }$or $x>4\mathrm{\pi }$.

Step 2. The Figure 30 is

Step 3. In the given figure Y1=5sinx+x  and  Y2=3

They have point of intersection

$x=0.52,x=3.18,x=5.71$

So the given equation has no further points of intersection (and therefore solutions) because both lines only cut on the given intersection point.

If there has any other point in which$Y_1\mathrm{and}{Y}_2$cut then they has more point of intersection.