Find the sinusoidal signal at specific frequency

[DODGEVIPER13]

Homework Statement

For a phasor V(x) = 8 + 4j find the sinusoidal signal that it represents if the frequency is 50 Hz?

Homework Equations

The Attempt at a Solution

sqrt(64+16)=8.944sin(50t) so clearly this is not correct?

 

[DODGEVIPER13]

8.944sin(100∏t+26.56)

 

[DODGEVIPER13]

where ω=2(pi)f=100(pi) and sin(ωt+θ) I found θ by tan^-1(4/8)=26.56°

 

[gneill]

where ω=2(pi)f=100(pi) and sin(ωt+θ) I found θ by tan^-1(4/8)=26.56°

8.944sin(100∏t+26.56)

Yup. That'll do it. Although strictly speaking you should indicate the units of the arguments to the sin function, since one is clearly radians and the other degrees...

 

[DODGEVIPER13]

8.944sin(100(pi)t+.463)

 

[DODGEVIPER13]

converted 26.56 to radians

 

[DODGEVIPER13]

oor would just doing 26.56°

 

[gneill]

Either way works. You're more likely to see the degrees version in practice.