Answer:
42° and 138°.
Step-by-step explanation:
Here we use the identity that
[tex]sin (x) = sin(180-x )[/tex].
Now, to find [tex]x[/tex], we make use of the inverse sine function:
[tex]x = sin^{-1}(0.0091)[/tex]
[tex]\boxed{ x = 42^o.}[/tex]
Another solution to this is
[tex]x_0= 180 -x= 180-42 \\\\\boxed{ x_0 = 138^o}[/tex]
Thus, the values of [tex]x[/tex] in the interval [tex]0<x<360[/tex] for which [tex]sin(x) =0.6691[/tex] are 42° and 138°.
