With the popular claims that the universe have more than 3 dimensions and With our current definition of trigonometric values , is it possible to extend this system in 4 Dimensions ,like we extended the system of real numbers into the complex plane ??
If yes, then what would the new trigonometric ratios be like ??
Would their values be still a real number or Would it be some sort of numbers we don't know??
The triangle would still have an opposite side, an adjacent side, and a hypotenuse. For instance, if you pick up a triangle from $2D$ space and lift it up into $3D$ space, the dimensions have changed, but the trig ratios are still the same. This applies to $4D$ as well.
The length of a line in 4D space (which can be extended to $n$-dimensional space as well) can be calculated as:
$$\sqrt{x_1^2+x_2^2+x_3^2+x_4^2}$$
and for the $n$-dimensional case you have:
$$\sqrt{x_1^2+x_2^2+x_3^2+ \cdots+x_n^2}$$