Answer:
[tex]\theta=337.2^o[/tex]
Step-by-step explanation:
we have
[tex]csc(2\theta+60^o)=4[/tex]
Let
[tex]x=(2\theta+60^o)[/tex] ----> equation A
so
[tex]csc(x)=4[/tex]
using a calculator
[tex]x=csc^{-1}(4)[/tex]
[tex]x=14.5^o[/tex]
substitute the value of x in the equation A
[tex](2\theta+60^o)=14.48^o[/tex]
Solve for angle theta
[tex]2\theta=14.48^o-60^o[/tex]
[tex]2\theta=-45.52^o[/tex]
[tex]\theta=-22.76^o[/tex]
The negative sign means that the angle theta lie on the IV quadrant
so
[tex]\theta=360^o-22.76^o=337.24^o[/tex]
