Trigonometric Problem Solving Using Identities

[Caldus]

First off, I'm not looking for answers, just trying to figure how I would solve certain problems.

If I had a problem such as:

sin A = -4/5
(-pie < A < -pie/2)
Using this, find cos A, tan A, cot A, sec A, csc A.

I know that I have to use identities, but how would I go about finding cos A? I can't find an identity that will allow me to find cos A using sin A -4/5. I guess I could use sin^2 -4/5 + cos^2 A = 1, but how would I solve that?

Also, I have absolutely no idea where to start with this problem:

-4cos((2x/3) - pie) + 2 = 0

Finally, which identity do I use for this problem:

tan(4x/5) = -1

Help much appreciated.

 

[NateTG]

Hmm:

Sin=Opposite/Hypotenuse=-4/5
Pythagoras: a²+b²=c²
Cos=Adjacent/Hypotenuse

 

[HallsofIvy]

To expand on NateTG's excellent suggestion:
Draw a right triangle with one angle at the origin of a coordinate system, one leg of length 4 (downward since we want "-4") and hypotenuse of length 4. Use the Pythagorean theorem to find the other leg. Once you know all three sides of the triangle, you can immediately calculate all the trig functions.

(NateTG? "Nate the great"?)