How do I find my angle using sin and cos values?

[Ascending One]

So, I have the values for sin (angle) and cos (angle)... how do I get back to my angle?

 

[Kurdt]

Use the inverse sin and cos functions.

 

[Ascending One]

But say my angle is 200. So I have inverse cosine(cosine (200)) which equals... 160. That's not what I want.

 

[HallsofIvy]

You can do either of two things:
1) Use, if only in your head, graphs for y= sin(x) and y= cos(x), draw horizontal lines at the value of sin(x) on the first and cos(x) on the second.

2) (And I think this is what you really want since I suspect you are requiring the angle be between 0 and 360) draw, again if only your head, a "unit circle" (circle on a coordinate system with center at (0,0) and radius 1) and remember that (cos(t),sin(t)) are the coordinates of the point at angle t, counter-clockwise around the circle from the positive x-axis. You can distinguish between the various values by looking at signs.
For your example, where sin(t)= -.3402 and cos(t)= -.9397, since both are negative, you are in the 3rd quadrant. You know immediately that t is between 180 and 270 degrees. Using "inverse sine", or arcsin, of -.3402 on a calculator (have made sure it is set to "degree mode"!) you get -20 degrees which is in the fourth quadrant. The corresponding angle in the third quadrant (20 degrees below the x-axis just as -20 is) is 180+ 20= 200 degrees. If I had used inverse cosine of -.9397, would have gotten 160 degrees, in the 2nd quadrant, 180- 160= 20 degrees above the x-axis. Knowing the the angle I want is in the 4th quadrant, I know it must be 20 degrees below the x-axis: 180+ 20= 200 degrees, again.

 

[Ascending One]

I used your method. Thank you!