Respuesta :

opposite side = sqrt  (3^2 - 2^2 ) =  sqrt5
sin theta = -sqrt 5 / 3   as the sine is negative in the 3rd quadrant 

csc theta = - 3 / sqrt5

The value of [tex]\rm Cosec \theta=\dfrac{-3}{\sqrt{5}}[/tex] if cos (theta) = -2/3 ; 180 < theta

What is the cosine angle?

The cosine of an angle of a right triangle is defined as the length of the side adjacent to the angle divided by the length of the hypotenuse of the triangle.

The given cosine angle is;

[tex]\rm Cos\theta=\dfrac{-2}{3}[/tex] 180 < theta < 270

The cosec angle is defined as;

[tex]\rm Cosec \theta=\dfrac{1}{sin\theta}\\\\ Cosec \theta=\dfrac{-3}{\sqrt{3^2-2^2} }\\\\ Cosec \theta=\dfrac{-3}{\sqrt{9-4} }\\\\Cosec \theta=\dfrac{-3}{\sqrt{5}}[/tex]

Hence, the value of [tex]\rm Cosec \theta=\dfrac{-3}{\sqrt{5}}[/tex] if cos (theta) = -2/3 ; 180 < theta < 270.

Learn more about trigonometry here;

https://brainly.com/question/22986479

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