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This means that you're invoking some function with an argument out of the function's domain. For example, the arcsine function requires an argument between -1 and +1, inclusive. If you try to take the arcsine of 2, you'll get this error.
If you require further assistance, please reply to this post and specify exactly what you're trying to do when you get this error.
You tried to use an argument to a function that was not in the function's domain. For example, the arcsine function takes an argument from negative one to positive one. Trying to take the arcsine of 2 will generate a domain error.
If you need further assistance, please specify the exact function and argument that is generating this error.
It seems that you are trying to calculate the inverse sine (arcsine) of 90. However the domain of definition of the arcsine function is the closed interval [-1, 1]. Any value outside of this interval will result in an error.
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[.
While the domain of the sine function is the whole of the real line, it range spans the interval [-1,1]. In other words the sine of an arbitrary angle is imperatively somewhere in the closed interval [-1,1]. So when you want to find the arc sine corresponding to a given value of a sine function, you cannot give as argument to the arc sine [sin^-1] a value that lies outside the interval [-1,1].
For your case, the argument is 60 and it is outside the permitted domain [-1,1]. That is why the calculator protests by signaling a domain error.
inverse sine (sin^-1) gives you the angle when the opposite side length and the hypotenuse, in relation to that angle, are given. therefore, if you want to do sin^-1(x), 0<x<1 for all real triangles
ex. sin^-1(1/2) would equal 30.
if you get a decimal, then go to [Mode] and select degrees instead of radians to get angle measures instead of radians... :)
I think you may find arcsin(x) is equivalent in older nomenclature to sin^-1 (x)...ie use the "2nd" and the SIN key instead of typing arcsin.
eg. arcsin(0.5) is 30 degrees is the same as sin^-1(0.5)
The ^-1 does not mean reciprocal, but "the angle whose sin is." Here the minus one indicates a kind of inverse operation. The word arcsin indicates that same inverse.