Question

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)

Answer 1

note: the possible answers are in sin, so we should map our phasors to sin

Answer 2

so we want to change the cos term at the end to a sin term ( and it should also have a positive amplitude )

Answer 3

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

Answer 4

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 )

Answer 5

= 10<30 + 10 < -135

= 10cos(30) + j 10sin(30) + 10cos(-135) + j 10sin(-135)

= 1.589 + j -2.071

Answer 6

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 )