How do you change the interval for a arc cos

Not quite true. (Explanation at the end)
The sine and cosine of an angle have values in the closed interval [-1,1]. That means whatever the value of the angle, its sine or its cosine cannot be less than -1 or greater than 1.
When you consider the inverse problem where you want to find the angle whose sine or cosine is known, you must take the values of the sine or cosine in the interval [-1,1]. That is the domain of the functions arc sine and arc cosine. So if you take a value outside the domain [-1,1], and want to calculate the angle to which it belongs, the calculator signals that there a domain error, because there is no angle that answers the question. Limit the arguments of the sin^-1 and cos^-1 to values in [-1,1]
For the inverses of arc tangent and arc cotangent functions there is no domain limitation because the range of tangent and cotangent is the whole real line ]-infinity, +infinity[.

In statistics, the range of 1-var a data set is the difference between the largest value and the smallest. R=Xmax-Xmin
In functions: the range of a function is the interval (or the Union of intervals) of the real line where the dependent variable takes it values.
Ex: sin(x). Whatever the value of the independent variable x, the values of the function sin(x) are in the closed interval [-1,1]. The range of the functions sin(x), and cos(x) is [-1,1].
No use of a calculator for finding the range of functions.

Does it refuse to do so or does it give an error message?
Three common errors:

1. Not having the correct angle unit. Wrong result, No error message
   
2. Confusing reciprocal of sine (1/sin(x) with arc sine (x) ,sin^-1(x). Confusing the reciprocal of cosine, 1/cos(x) with arc cosine (cos^-1(x)). Wrong result, No error message
   
3. Taking the argument of the inverse sine and/or inverse cosine functions outside the interval [-1,1]. This gives a domain error.
   

If you are trying to calculate arcsine (sin^-1) and arccosine (cos^-1) the only whole number you can use are -1,0 and 1. This due to the fact that the domain of these functions is the closed interval [-1,1]. Any value outside that interval will trigger an error message. No limitation on the argument of the arc tangent or arc cotangent functions

If the angle unit is set to degree the arc will be in degrees, and if angle unit is radian, the arc will be in radians.

What were you doing when that error occurred? No, i am not asking for your alibi. It helps to narrow down the possibilities. Anyway, I think you might have asked the calculator to calculate a function at a value for which it (the function) is not defined. An example is the arc cosine or arc sine. They are defined on the closed interval [-1,1]. If you ask the calculator to evaluate cos^-1(3.45) you will get a domain error because the argument 3.45 is not within the domain [-1,1] of the arc cosine function.

Is there a question? Why so secretive, spill it out.
To access the arc cosine (cos^-1) press 2nd COS and enter the argument. Make sure you are within range, because the domain of arc cosine is from -1 to +1. Any value outside of this closed interval will warrant a DOMAIN ERROR.

The key sequence [2nd] [Cos] calls the function arcosine or cos^-1. However that function takes its values in the range of the cosine function which is the interval [-1,1].
As you can see, your value of 1301.16 is clearly outside the interval [-1,1].

Since you are familiar with sines, cosines, you know that their ranges (interval of values) varies from -1 to 1. The inverse functions of sine and cosine tkae their values in that very domain, [-1,1].
However you fed the arc sine function (sin^-1) a vlaue of (25/20.48) and that value is obviously larger outside the [-1,1] domain, hence the DOMAIN error message.

No such domain limitations exist for arc tangent (tan^-1) because the range of the tangent function spans the open interval ]negative infinity to positive infinity[.

You are indeed committing an error. The sequence [2nd][COS] is activating the function arcosine or arccos or cos^-1, the inverse of the cosine function. If you remember the properties of the cosine functions, you know that cos(x) is defined over the real line ]- infinity to infinity[, but its range spans the interval [-1,1].
Since the arcosine function is the inverse of the cosine, its domain of definition is the range of the cosine, namely the closed interval [-1,1].

Thus if you enter [2nd][COS][3180.04] the calculator flags this as a domain error, because 3180.04 is outside the interval [-1,1]

Restrict the argument of cos^-1 to any value inside the closed interval [-1,1].
When manipulating the trigonometric functions and their inverses you must keep in mind that the results you get are dependent on the angle unit your calculator is configured for (deg, rad).

The cosine function takes its value on the whole real line, the angle domain spans ]-infinity, + infinity[. The range of the function is however limited to the [-1, +1] interval.
Thus if you want to calculate the arc (angle) from the value of the cosine, the cosine must be in the interval [-1, +1]. Any value outside this domain will give you a domain error.
Check that the values you feed to the arc cosine function are in the interval [-1,+1].

If the angle unit is the degree the value returned bay [cos^-1] is in degrees, and if the angle unit is the radian, the value returned is in radians