Question

A sinusoidal source is usually described by the function cos(ωt+ϕ), where the units of the frequency ω are radians/second and the units of the phase angle ϕ are degrees. this means that the product ωt has the units radians, which cannot be added to the phase angle in degrees. to evaluate the value of the sinusoidal source at a given time, you must transform the product ωt to degrees or the phase angle to radians before performing the addition in the cosine argument. if the voltage source is given by v(t)=50cos(2000t−45∘) mv, find v(392.7 μs). express your answer with the appropriate units.

Answer 1

49.999999999999974312306505198184 V

Explanation:

Step 1: you see 45°, which gives you a easy conversion
`\frac \pi 4`).

Now,
`t = 392.7 \mu s = 392.7* 10^(-6) s`, start replacing.

`V= 50 cos ( 2* 10^3 * 392.7 *10^(-6) -\frac \pi 4) = 50 cos (0.7854 - \frac \pi 4) =\\ 49.999999999999974312306505198184 V`