Question

If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?

Answer 1

In degrees you're bounds are between 180 and 270 degrees.

Answer 2

Between 180 and 270 puts you in Quadrant III, like this with the sin of your angle:

Answer 3

If sin is opposite over hypotenuse, here is your angle in the plane:

Answer 4

That is actually a 60 degree reference angle. Anyway...now that have that set up like that, we can find the other values you are looking for.

Answer 5

Cos theta is equal to the side adjacent over the hypotenuse, like this:

Answer 6

cos Θ = negative 1 over 2; tan Θ = square root 3
is this the answer?

Answer 7

Tan theta is the sin/cos. We have that in a fraction over a fraction form. We will reduce: