Question

Voltage = V1=3sin(wt) V2=cos(wt) V3=v1+v2
Find the expression in sine waveform v3=Rsin(wt+phase angle)
verify the resultant voltage is in the same frequency as v1 and v2


W= Waveform

Answer 1

Answer on Question #82579 – Math – Trigonometry

Question

Voltage $V1 = 3 * \sin(wt)$, $V2 = \cos(wt)$, $V3 = V1 + V2$

Voltage = V1 = 3 sin(wt) V2 = cos(wt) V3 = v1 + v2

Find the expression in sine waveform v3 = Rsin(wt + phase angle)

verify the resultant voltage is in the same frequency as v1 and v2

W = Waveform

Solution

$$V3 = 3 * \sin(wt) + \cos(wt) = \sqrt{10} \left( \frac{3}{\sqrt{10}} \sin(wt) + \frac{1}{\sqrt{10}} \cos(wt) \right) \\ = \sqrt{10} \left( \sin \left( wt + \arcsin \left( \frac{\sqrt{10}}{10} \right) \right) \right)$$

Answer: $\sqrt{10} \left( \sin \left( wt + \arcsin \left( \frac{\sqrt{10}}{10} \right) \right) \right)$.

Answer provided by https://www.AssignmentExpert.com