acos(x) returns complex values. Why do they describe ?

In my code the acos function returns complex values because my input x is not in range [-1 1]. But why do these complex values describe ?

Answer 1

[Ameer Hamza]

But why do these complex values describe?

To understand this, you need to study calculus. This is not just limited to cos(), all trigonometric functions exhibit this behaviour. In short, the domain of trigonometric functions can be extended to the complex plane, in which case the range of those functions will also span the complex plane (instead of usual [-1, 1]). The following are some links to show how trigonometric functions and complex numbers are interconnected

https://en.wikipedia.org/wiki/Euler%27s_formula

https://en.wikipedia.org/wiki/Taylor_series

https://www.livescience.com/51399-eulers-identity.html

https://en.wikipedia.org/wiki/Sine#Relationship_to_complex_numbers