Question

If sin θ = 1 over 3 and tan θ < 0, what is the value of cos θ?

2 square root of 2 over 3
negative 2 square root of 2 over 3
2 square root of 2
negative 2 square root of 2

Answer 1

2√2 / 3 (first answer choice)

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