Question

急！化简三角函数

sin(-9/4π) + cos(-9/4π) + tan(-9/4π)
为什么要加+4π？

Answer 1

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

Answer 2

=sin(-1/4π) + cos(-1/4π) + tan(-1/4π)
=-sin(1/4π) + cos(1/4π) - tan(1/4π)
=-1

Answer 3

sin(-9/4π) + cos(-9/4π) + tan(-9/4π)
=sin(-9/4π+2π) + cos(-9/4π+2π) + tan(-9/4π+2π)
=sin(-1/4π) + cos(-1/4π) + tan(-1/4π)
=-sin(1/4π) + cos(1/4π) - tan(1/4π)
=-√2/2+√2/2-1
=-1