Amplitude, Time Period, Frequency, Phase Angle, and Current Calculation

Answer
a)
1

i = 38 sin (350πt − 2.7)
Amplitude of sine wave
w = A sin Bt − C + D
is A.
Therefore, amplitude of i is
Amp. = 38
b)
Time period of a sine wave is
T = 2π
B = 2π
350π = 5.71 ms
c)
Frequency of sine wave is
ω = B = 350π Hz
d)
Initial phase angle is
φ = C
B = 2.7
350π = 2.46 × 103
So the phase angle is
2.46 × 103 rads or 0.14◦
to the right.
e)
when t = 8.6 sec
i = 38 sin 350π × 8.6 − 2.7 = −16.24 A
f ) The current first reaches its maximum value when
sin (350πt − 2.7) = 1 or 350πt − 2.7 = π
2
implies
tmax = 27.19 ms
2

a)
sin (A + 180) = sin A cos 180 + cos A sin 180 = − sin A
b)
3