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

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

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

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

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