Answer: The answer is (C) Quadrant III.
Step-by-step explanation: We are given to determine the quadrant when the terminal side of the angle lies according to the following conditions: tan (t) > 0, csc (t) < 0.
We know that
In Quadrant I, all the trigonometric ratios are positive (greater than 0).
In Quadrant II, only sine and co-secant ratios are positive.
In Quadrant III, only tangent and cotangent ratios are positive.
In Quadrant IV, only the cosine and secant ratios are positive.
According to the given condition,
tan (t) is positive - Quadrant I or Quadrant III
and
csc (t) is negative - Quadrant III or Quadrant IV.
Taking the common quadrant, the resulting quadrant will be Quadrant III.
Thus, (B) Quadrant III is the correct option.
