Question

If sin 0(theta)=2/3 and tan 0(theta)<0. What is the value of cos 0(theta)

Answer 1

Answer:

cos Ф = adj / hyp = √5 / 3

Step-by-step 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