Question

If sin Θ = 2/3 and tan Θ < 0, what is the value of cos Θ?

Answer 1

Answer:If sin Θ is positive and tan Θ is negative, then the angle should be in the second quadrant using the rule of thumb. In this case, cos Θ is expected to be negative.

Step-by-step explanation:If sin Θ is positive and tan Θ is negative, then the angle should be in the second quadrant using the rule of thumb. In this case, cos Θ is expected to be negative.

Answer 2

cos Ф = adj / hyp = √5 / 3

Explanation:

If sin Ф is +, then Ф must be in either Quadrant 1 or Quadrant 2.

If tan Ф < 0, then Ф must be in either Quadrant 2 or Quadrant 3.

So we conclude that Ф is in Quadrant 2.

If sin Ф = opp / hyp = 2/3, then opp = 2 and hyp = 3, and adj is found using the Pythagorean Theorem:

adj = √( 3² - 2² ) = √( 5 )

With adj = √5 and hyp = 3, cos Ф = adj / hyp = √5 / 3