Given the following function:

$f(x)=sin(x)+x^2-2$

a$)(25\%)$ Find the root using Newton$-$Raphson method. No tolerance is given, please make only $3$ iterations, use an initial guess of $x_0=0.$ Use $4$ decimal places and compute relative approximate percent error at each iteration. Please make a table. Solutions without tables will not be graded. $($Hint: You must use radians in your calculations$)$

b$)(10\%)$ With an initial guess of $x_0=-0\mathrm{.}45,$ this method will definitely NOT work as fast as above. Why? Explain WITHOUT solving the problem with the new initial guess.