Question

If sin Θ = 3/5 and tan Θ > 0, what is the value of cos Θ?

Answer 1

\(\Large\rm \sin\theta\) is positive.
\(\Large\rm \tan\theta\) is positive.

So using that information, what `quadrant` is our angle theta in?

Answer 2

Quadrant 1?

Answer 3

hello?

Answer 4

Mmm good!
So that let's us know that \(\Large\rm \cos\theta\) will be positive also.

Answer 5

If we draw a triangle in the first quadrant

Answer 6

We can use the sine information to label the sides.

Answer 7

\[\Large\rm \sin \theta=\frac{opposite}{hypotenuse}=\frac{3}{5}\]

Answer 8

How does that help for the Cosine?

Answer 9

You can find the missing side of the triangle by using the `Pythagorean Theorem`.

Then you can easily find cosine by using your relationship,\[\Large\rm \cos \theta=\frac{adjacent}{hypotenuse}\]

Answer 10

Wait, whats the Adjacent? That's the last part I dont get