Reversing the question
Sine takes an angle and gives a ratio; arcsine takes that ratio and gives back the angle. arcsin(0.5) = 30° — the angle whose sine is exactly 0.5. Similarly, arccos(0.5) = 60° — the angle whose cosine is exactly 0.5.
Why arcsine and arccosine have a restricted input range
Sine and cosine only ever produce values between -1 and 1 — no angle has a sine or cosine of, say, 2. So arcsine and arccosine only accept inputs in the -1 to 1 range; anything outside it has no real angle to return.
Why arctangent has no such restriction
Tangent itself can take any real value — it grows without bound as the angle approaches 90°. Because tangent's output range is unrestricted, arctangent accepts any real number as input.
Choosing degrees or radians for the answer
The angle these functions return can be shown in either degrees or radians — the same underlying angle, just in whichever unit is more convenient, using the same conversion factor covered in the companion article on degree-radian conversion.