if cosФ<0 and tg Ф>0; then we are in the third quadrant, then sin Ф<0
Fundamental realtion of trygonometry:
sin²Ф+cos²Ф=1
Then:
sin Ф=⁺₋√(1-cos₂Ф):
Because we are in the third quadrant; sin Ф=-√(1-cos²Ф)
Sin Ф=-√(1-(-2/5)²)=-√(1- 4/25)=-√(21/25)=-√21 / 5
Answer: sin Ф=-√21 / 5