Originally Posted by

**Blodwynne** It's one of those trigonometric ones that always make my brain go huh?

If cos x= (-4/5) and tan x>0, find the value of Sin x.

I figured that since Cos was negative, it was in either quadrants II or III. Since Tan is positive, it must be in III. After that....I get lost.

~Wynne

Think of a right triangle. The cosine of an angle is the ratio of the adjacent side to the hypotenuse. So, ignoring the negative for now:

Code:

/|
5 / |
/ | b
/ |
/ θ |
----------
4

By the Pythagorean theorem, we have

(this is a Pythagorean triple: all sides are integers).

Now, , so we have

.

But, our is in quadrant I. Adding to get into quadrant III will make the sine negative: