Question

does the sign of a number change when it's reciprocal is taken

Answer 1

sin values are (0), (1/2), (1/√2), (√3/2) and (1) and the reciprocal of sin is cos and the values of cos is 1, (√3/2), (1/√2), (1/2), and (0).
yes the values of sin will affect when taken its reciprocal