How Does Phasor Addition Simplify Trigonometric Expressions?

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The discussion focuses on simplifying the expression x(t)=5cos(wt)+5cos(wt+120)+5cos(wt-120) using phasor addition. Participants note that when applying the phasor addition rule, the result simplifies to zero. This indicates that the combined effect of the three cosine terms cancels out completely. The final conclusion is that x(t) can be expressed as x(t)=0. The use of phasors effectively demonstrates how trigonometric expressions can be simplified.
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Homework Statement


Define x(t)=5cos(wt)+5cos(wt+120)+5cos(wt-120)

simplify x(t) into the standard sinusoidal form:x(t)= A cos(wt+phase).Use phasors to do the algebra.

Homework Equations


The Attempt at a Solution


i know it needs to use phasor addition rule.
First,i represent x1(t),x2(t),x3(t) by the phasors,and then add them together
however the result is 0,then i don't know to dothanks a lot:))
 
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smallwa said:

Homework Statement


Define x(t)=5cos(wt)+5cos(wt=120)+5cos(wt-120)

Correct x(t), please!


ehild
 
ehild said:
Correct x(t), please!


ehild

sorry,corrected
 
The result is really zero. So write x(t)=0.

ehild
 
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