Calculate for a sinusoidal signal with an angular velocity of 314.1593 radians/s and a peak voltage of 340 V

Question

Calculate for a sinusoidal signal with an angular velocity of 314.1593 radians/s and a peak voltage of 340 V

The instantaneous amplitude at t = 15 ms

V(t) = A.sin(ω.t)

V(t) = 340 sin (314.1593 x 15 x 10-3)

V(t) = 340 sin (4.71)

V(t) = 340 * -1 = -340 V

This is the solution found in my textbook. On the last line why do you multiply by -1?

Answer 1

In general, these quantities are expressed in units of radian. We can express $\sin (4.71^c)$ where $c$ generally denotes radian measure as, $\sin (4.71\times \frac{180}{\pi}) \approx \sin(270^\circ) = -1$. Hope it helps.