Question

If cos Θ = and tan Θ > 0, what is the value of sin Θ?

Answer 1

It appears there was a mis-transition of information, cosine of theta = (no number).
Could you fill in the missing detail?

Answer 2

-2/5

Answer 3

We should start with drawing a picture of a triangle given the angle theta. Knowing that \( \cos \theta = - \dfrac{2}{5} \) tells us the adjacent side length and the hypotenuse. Because tangent is positive, both sine and cosine are negative so that tan = sin / cos, the signs cancel. Thus our picture looks like this:


Is that part clear?

Answer 4

yes

Answer 5

The hypotenuse is always a positive value, so we consider negative values of cosine and sine as going in the negative direction on the graph. We went left because -2 is to the left of 0, and down because sin is also negative.

So with that, we have to use Pythagorean theorem to find the remaining side, which is opposite of angle \( \theta \).
Then we use:
\( \sin \theta = \rm \dfrac{opposite}{hypotenuse} = -\dfrac{?}{5} \)

Answer 6

ok