已知正弦交流电压U1=6 2 sin(100∏t+90°)V,U2=82 sin(100∏t)V,试计算:(1) U1+U2 (2) U1-U2

题目

已知正弦交流电压U1=6 2 sin(100∏t+90°)V,U2=82 sin(100∏t)V,试计算:(1) U1+U2 (2) U1-U2
问题中6和8后面均有一个根号,100后面是派.

答案

(1)U1+U2=
6*根号2sin(100派t+90)+8*根号2sin(100派t)
=-6*根号2cos(100派t)+8*根号2sin(100派t)
=10*根号2[-3cos(100派t)/5+4sin(100派t)/5]
=(10*根号2)*sin(100派t-53度)
(2)U1-U2
6*根号2sin(100派t+90)-8*根号2sin(100派t)
=-6*根号2cos(100派t)-8*根号2sin(100派t)
=-10*根号2[3cos(100派t)/5+4sin(100派t)/5]
=-(10*根号2)*sin(100派t+53度)