The general equation for a sinusoidal wave is:
y = A sin(2πft + φ)
where A is the amplitude, f is the frequency, t is time, and φ is the phase angle.
Given the parameters f = 1 kHz, A = 2 V, and φ = -π radians, we can plug them into the general equation to get:
y = 2 sin(2π × 1 kHz × t - π)
Simplifying, we get:
y = 2 sin(2000πt - π)
Comparing the equation with the options given:
a. 1sin(2π5t - π) - This equation has a frequency of 5 Hz, not 1 kHz.
b. 2sin(2π1000t - π) - This equation matches the given parameters and is correct.
c. 1sin(2π1000t) - This equation has an amplitude of 1 V, not 2 V.
d. 2sin(2π1t + π) - This equation has a frequency of 1 Hz, not 1 kHz, and the phase angle is positive, not negative.
Therefore, the correct sinusoidal equation is:
y = 2 sin(2π × 1 kHz × t - π), which is option b.