Verified Answer :

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

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