Trigonometric Functions

@Sakib Nazmus , you should use a backslash " \ " for functions such as \sin $\sin$ , \cos $\cos$ , \tan $\tan$ , \ln $\ln$ , \gcd $\gcd$ , \int $\int$ , \sqrt x $\sqrt x$ , \sum $\sum$ . Then the space after the function is automatic (always remember LaTex creators are not stupid). Note that function should not appear italic which are for variables and constants. For example sin x $sin x$ -- note that all letters are italic and stick together despite separated by a space. Now \sin x $\sin x$ -- note only $x$ is italic and the space.

I think you mean $x^2=1-y^2$ instead of $x^2=\sqrt{1-y^2}$