Answer:
-(√105)/11
Step-by-step explanation:
Tangent is the ratio of sine to cosine. When tangent is positive, sine and cosine have the same sign. This means the appropriate choice will be either the first one or the last one.
cos(θ) = -√(1 - sin(θ)²) . . . . in the 3rd quadrant
... = -√(1 - (-4/11)²)
... = -(1/11)√(121 -16)
... = -(√105)/11 . . . . . . matches the first selection
