In the third quadrant, tan is positive and cos is negative. Quadrant is a circle divided into four potion in which in each portion some of the trigonometry function are positive and others negative. This is important in determining and converting any negative angle to positive value. The value of the angle in the third quadrant is represented as (180+theta) where theta is the angle given in question.
Note that all the trigonometry values are all positive in the first quadrant thereby making tan positive in the first quadrant. Also, the only value positive in the third quadrant is tan making both sin and cos negative.
