急!化简三角函数sin(-9/4π) + cos(-9/4π) + tan(-9/4π)为什么要加+4π？

sin(-9/4π) + cos(-9/4π) + tan(-9/4π)
=sin(-9/4π+4π) + cos(-9/4π+4π) + tan(-9/4π+3π)
=sin(7/4π) + cos(7/4π) + tan(3/4π)
=sin(1/4π)-cos(1/4π)+tan(3/4π)
=根号2/2-根号2/2-1
=-1