The value of the angle θ is 160.52° then the value of the cosine will be negative 0.9428.
Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Angle θ is in standard position.
If sin(θ) = − 1/3 , and π < θ < 3π/2
Then the angle will be
[tex]\theta = \sin ^{-1}\dfrac{-1}{3}\\\\\theta = -19.47[/tex]
Then add 180 degrees, then we have
[tex]\theta = -19.47 + 180\\\\\theta = 160.52[/tex]
Then the value of the cosine will be
[tex]\cos 160.52^o=-0.9428[/tex]
More about the trigonometry link is given below.
https://brainly.com/question/22698523
