# Find the sinusoidal signal at specific frequency

## Homework Statement

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

## The Attempt at a Solution

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

## Answers and Replies

8.944sin(100∏t+26.56)

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

gneill
Mentor
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...

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

converted 26.56 to radians

oor would just doing 26.56°

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