Respuesta :

Answer:

C

Step-by-step explanation:

cosecΘ = [tex]\frac{1}{sin0}[/tex] = [tex]\frac{2}{\sqrt{3} }[/tex] ( cross- multiply )

2sinΘ = [tex]\sqrt{3}[/tex] ( divide both sides by 2 )

sinΘ = [tex]\frac{\sqrt{3} }{2}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{2}[/tex] ) = 60°

Answer:

C.  60°

Step-by-step explanation:

by definition,  cosec(θ) is the reciprocal of sin(θ)

In other words ,

[tex]\text{cosec} \left( \theta \right) =\frac{1}{\sin \theta }[/tex]

Then

[tex]\text{cosec} \left( \theta \right) =\frac{2}{\sqrt{3} }[/tex]

[tex]\Longleftrightarrow \frac{1}{sin \left( \theta \right) } =\frac{2}{\sqrt{3} }[/tex]

[tex]\Longleftrightarrow sin \left( \theta \right) =\frac{\sqrt{3} } {2}[/tex]

Then

θ = 60°

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