Answer:
1.568, 3.432, 11.568, 13.432
Step-by-step explanation:
Divide equation [tex]6\sin\left(\dfrac{\pi }{5}x\right)=5[/tex] by 6:
[tex]\sin\left(\dfrac{\pi }{5}x\right)=\dfrac{5}{6}.[/tex]
Then
[tex]\dfrac{\pi }{5}x=(-1)^k\arcsin\left(\dfrac{5}{6}\right)+\pi k,\ k\in Z,[/tex]
[tex]x=(-1)^k\dfrac{5}{\pi }\arcsin\left(\dfrac{5}{6}\right)+5k,\ k\in Z.[/tex]
Since [tex]\arcsin\left(\dfrac{5}{6}\right)\approx 56^{\circ}\approx \dfrac{\pi }{3.2},[/tex]
four smallest positive solutions are
1. [tex]\dfrac{5}{3.2}\approx 1.568,\ k=0;[/tex]
2. [tex]\dfrac{-5}{3.2}+5\approx 3.432,\ k=1;[/tex]
3. [tex]\dfrac{5}{3.2}+10\approx 11.568,\ k=2;[/tex]
4. [tex]\dfrac{-5}{3.2}+15\approx 13.432,\ k=3.[/tex]
