How to calculate the .707 value used in rms voltage

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The .707 value used in calculating RMS voltage (Vrms = Vp * .707) is derived from the square root of 2 divided by 2, specifically for sine waves. This value represents the RMS for a sine wave, which can be calculated through integration of V(t)² over one complete cycle, followed by dividing by the cycle time and taking the square root. The discussion emphasizes that .707 is not applicable to all waveforms, but specifically to sine waves. Understanding this calculation is essential for accurate voltage measurements in AC circuits. The mathematical foundation is crucial for those seeking to grasp RMS voltage concepts.
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I need help, and can't find anywhere how to calculate the .707 value using calculus. The value used when calculating Vrms =Vp*.707, i need to know how to calculate the .707. Any help would be great, Thanks!

Scott
 
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.707 is for a sine wave only, and you could determine it by taking the integral of V(t)2 over a full cycle, dividing by the time of the cycle, and then taking the square root of the answer (hence the name "root mean square").
 
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