# Math Help - simplify expression of sine

1. ## simplify expression of sine

How do you answer this one.

What is the complex expression for a given alternating current,
$i = 250sin(\omega t - 25 ^ \circ)$

a. 227 + j106
b. 160 - j75
c. 227 - j106
d. 160 + j75

2. For the current
$A\sin(\omega t + \phi)$
The amplitude is $A$ and phase angle is $\phi$.
For this problem $A = 250$ and $\phi = -25^o$.

I think the complex expression being asked is the one with the given amplitude and phase angle.
This is $a + jb$ with
$a^2 + b^2 = A^2$ and
$b/a = tan(\phi)$

So the answer is closest to (c): $227 - j106$