Suppose cotangent of theta is equal to 5 over 12 , where pi is less than theta comma theta is less than 3 pi over 2 What is sine of theta ?

Since cotangent is cos θ divided by sin θ, cot θ = 5/12 gives the ratio of the horizontal coordinate to the vertical coordinate as 5:12. In the third quadrant, both coordinates are negative, so sine is negative. The hypotenuse is √(5² + 12²) = 13, making sin θ = −12/13, choice D.

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