You are a sophomore, and you can't learn much theory in high school. I will give you a conclusion. The expression of infinite series of sine function is:

sinx=x-x^3/3！ +x^5/5！ -x^7/7！ +x^9/9！ -... the ellipsis extends to infinity.

n！ It's called factorial, n = n (n-1) (n-2) (n-3) ... 4x3x2x1,3! =3*2* 1=6

So knowing the value of sin is equivalent to assigning a value to the following infinite polynomial, so you should choose the accuracy of calculation, because infinite term cannot be calculated, and computer intelligence handles the calculation of finite term polynomial.

If you want to calculate by hand, you can get sinx ≈ x-x 3/3 at most! If sinx is small enough, then sinx≈x can be calculated manually with cubic terms when it is large. If there is a formula for finding the root of cubic equation, the quintic term cannot be calculated by hand. Theoretically, it is proved that there is no specific formula available, so you can only use a computer for interpolation approximation to find a solution with certain accuracy.

I'm not familiar with BASIC, but it shouldn't be difficult to solve it by polynomial programming.