anonymous
  • anonymous
Perform the following operation and determine an expression for e(t); e(t)=10sin(wt +30degrees)-10cos(wt -45degrees) options are; 1.e(t)=0 2.e(t)=2.61sin(wt-52.5degrees) 3.e(t)=18.7sin(wt-17.2degrees) 4.e(t)=4.8sin(wt+36)
Mathematics
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anonymous
  • anonymous
Perform the following operation and determine an expression for e(t); e(t)=10sin(wt +30degrees)-10cos(wt -45degrees) options are; 1.e(t)=0 2.e(t)=2.61sin(wt-52.5degrees) 3.e(t)=18.7sin(wt-17.2degrees) 4.e(t)=4.8sin(wt+36)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
note: the possible answers are in sin, so we should map our phasors to sin
anonymous
  • anonymous
so we want to change the cos term at the end to a sin term ( and it should also have a positive amplitude )
anonymous
  • anonymous
if we draw a graph of y=-cos(x) , we can see , geometrically , that this is the same graph as y=sin(x) but shifted to the right 90 degrees ( and to cause this shift we would need to subtract 90 from the arguement of the -cos function, to get a +sin function

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anonymous
  • anonymous
so v(t) = 10sin(wt +30 ) + 10 sin ( wt -45-90 ) v(t) = 10sin(wt+30) +10sin(wt -135) now, converting to phasors ( where "r < x " means amplitude r at an angle of x )
anonymous
  • anonymous
= 10<30 + 10 < -135 = 10cos(30) + j 10sin(30) + 10cos(-135) + j 10sin(-135) = 1.589 + j -2.071
anonymous
  • anonymous
2.61< -52.5 convert back to time domain, remember our phasors mapped to sin functions so v(t) = 2.61 sin (wt -52.5 )

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