Answer:
2√2 / 3 (first answer choice)
Step-by-step explanation:
If tan Ф < 0, then Ф must be in either Quadrant II or Quadrant IV.
If sin Ф = +1/3, then Ф (for this problem) is in Quadrant II.
Remembering that sin Ф = opp / hyp = 1 / 3, we use the Pythagorean Theorem to find the adj side:
adj² + 1² = 3², or
adj² + 1 = 9, or adj² = 8. Since Ф is in Quadrant II, adj is negative.
The value of cos Ф = adj / hyp = √8 / 3 = 2√2 / 3
