How do you solve this?

[Student123]

Solve csc(x/3) = 1.5.
1/(sin(x/3)=1.5 <=> sin(x/3)=2/3
So far I've got x1/3=sin^-1(2/3)=0.7297 <=> x1=2.189.
But then I don't know how to find the next x value, I've tried x2=pi-x, but according to Desmos it's the wrong answer.

 

[Dr.Peterson]

You have to take the supplement before multiplying by 3, immediately after using the inverse sine.

That is, you found that one solution for x/3 is sin^-1(2/3)=0.7297; another is pi - 0.7297. Now multiply that by 3.

 

[Student123]

Ohhh, I see! That's why there's a difference between the reference angle and the first angle. Thank you!