Given that secant theta is equal to negative 37 over 12 , what is the value of cotangent theta , for pi over 2 is less than theta comma theta is less than pi ?

Since secant is the reciprocal of cosine, cos θ = −12/37. Because θ is between π/2 and π, it is in Quadrant II, where sine is positive; using sin² θ + cos² θ = 1 gives sin θ = 35/37. Therefore cot θ = cos θ/sin θ = (−12/37)/(35/37) = −12/35, which is choice B.

AI-written and checked against the verified answer.