How do I get my angle?

1. Mar 3, 2008

Ascending One

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

2. Mar 3, 2008

Kurdt

Staff Emeritus
Use the inverse sin and cos functions.

3. Mar 3, 2008

Ascending One

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

4. Mar 3, 2008

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.

5. Mar 3, 2008

Ascending One

I used your method. Thank you!