The function arctan (x) is defined for all real values of x.
Why is the above statement true? Also, is there some way I could logically deduce the answer without using a calculator or basing my answer on memorization?
Why is the above statement true? Also, is there some way I could logically deduce the answer without using a calculator or basing my answer on memorization?
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The statement is true. The range of tan(x) is the domain of arctan(x). Since tan(x) can equal all real values of x, then the domain of the arctan function is all reals.
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Arctan(x) means "the angle whose tangent is x."
Now, the tangent function, if graphed, ranges over the entire real number line. I think this is the appropriate way to understand why the statement is true.
Now, the tangent function, if graphed, ranges over the entire real number line. I think this is the appropriate way to understand why the statement is true.