Q: cos^-1(-3.48), why is the calculator say invalid argument?

 

Because -3.48 is way out of range.

cos(x) must be -1 ..... +1, inclusive, so -3.48 is impossible.

 

cosine can be described the ratio of two sides of

a right-angled triangle, cos = adj/hyp,

and hypotenuse is always the longest side.

This means the ratio |adj/hyp| cannot exceed 1.

 

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Because the question is asking for what angle is the cosine equal to -3.48.  Since the cosine of any angle must lie between the values of ±1, there is no angle for which the cosine can be -3.48.

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