Question

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

Is the answer sqr(5) / 3??

Answer 1

yes

Answer 2

So let's first determine which quadrant we're in.
Sine is positive,
Tangent is negative.
That put's us in quadrant 2.

Answer 3

ok

Answer 4

Understand how I was able to label these sides using the sine information?

Answer 5

yes.

Answer 6

So I'm assuming you applied the Pythagorean Theorem and found that the missing side must be sqrt5.

But understand, you use that theorem to get a length.
It doesn't really tell you about direction.
Should the value be positive or negative if we're in quadrant two.
(Realize that this length is in the x direction)

Answer 7

I did, and since I'm finding cosine, that's adjacent / hypotenuse. So wouldn't it come out to be sqr(5) / 3?

Answer 8

The square root 5 side should be negative.
Understand why?

Answer 9

Yes because it's in a Quadrant which tells us i'ts negative.

Answer 10

So it's -sqr(5) /3 :)

Answer 11

@zepdrix

Answer 12

Yah there we go! ^^

Answer 13

Thanks again! You're the best :)