In the interval
[tex]0\leq x<2\pi[/tex]
We have two values that sin is negative. I will draw a trigonometric circle:
We can find these values using a calculator.
[tex]x\text{ = }\sin ^{-1}(-0.36)[/tex]
This will give -21.1 degrees. If we start counting from zero, one complete circle is 360 degrees. So to find x2 we have to do:
[tex]x2\text{ = 360 - 21.1 = 339 degr}ees[/tex]
And to find x1 we have to add 21.1 degrees counting from the start that is now 180:
[tex]x1=180+21.1\text{ = 201.1 degre}es[/tex]
We do this process because we have two angles that give the same sin value, and they are symmetric compared to the sin axis!
