Since the zeros of sin x are O,±π,±2π,…,we can factorize sin x: sin x=ax(x-π) (x+π) (x-2π) (x+2π) … and using limx→0sinx/x=1 we can determine the value of a:sinx=x· (1-x/π)· (1+x/π)·...Since the zeros of sin x are O,±π,±2π,…,we can factorize sin x: sin x=ax(x-π) (x+π) (x-2π) (x+2π) … and using limx→0sinx/x=1 we can determine the value of a:sinx=x· (1-x/π)· (1+x/π)· (1-x/2π)·(1+x/2π)…=x· (1-x2/π2)· (1-x2/(2x)2)· (1-x2/3π)2…展开更多
文摘Since the zeros of sin x are O,±π,±2π,…,we can factorize sin x: sin x=ax(x-π) (x+π) (x-2π) (x+2π) … and using limx→0sinx/x=1 we can determine the value of a:sinx=x· (1-x/π)· (1+x/π)· (1-x/2π)·(1+x/2π)…=x· (1-x2/π2)· (1-x2/(2x)2)· (1-x2/3π)2…
