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

Cos

θ

=

√

5

3

or it could be cos

θ

=

√

5

-

3

Explanation:

Since sin

θ

is negative, it can be in the third or fourth quadrant

Drawing your right-angled triangle, place your

θ

in one of three corners. Your longest side will be 3 and the side opposite the

θ

will be - 2. Finally, using Pythagoras theorem, your last side should be

√

5

Now, if your triangle was in the third quadrant, you would have

cos

θ

=

√

5

-

3

since cosine is negative in the third quadrant

But if your triangle was in the fourth quadrant, you would have

cos

θ

=

√

5

3

since cosine is positive in the fourth quadrant

Answer: - sqrt 5 / 3