Which numerical value represents the multiplier used with a 45 degree offset?

Which numerical value represents the multiplier used with a 45 degree offset?

• A. 1.41
• B. 1.00
• C. 1.73
• D. 2.00

Answer: (A)

When a signal has a 45-degree phase offset between two equal-magnitude components, those components add in a way that increases the overall peak value by a factor of sqrt(2). You can see this by writing the signal as A cos(ωt) + A sin(ωt). Using the identity cos x + sin x = sqrt(2) cos(x − 45°), the maximum value becomes A times sqrt(2). So the multiplier for a 45-degree offset is sqrt(2), which is about 1.41. This also aligns with the common RMS-to-peak relationship for a sine wave, where peak = RMS × sqrt(2). The other numbers don’t fit because they correspond to no offset or different geometric outcomes.

When a signal has a 45-degree phase offset between two equal-magnitude components, those components add in a way that increases the overall peak value by a factor of sqrt(2). You can see this by writing the signal as A cos(ωt) + A sin(ωt). Using the identity cos x + sin x = sqrt(2) cos(x − 45°), the maximum value becomes A times sqrt(2). So the multiplier for a 45-degree offset is sqrt(2), which is about 1.41. This also aligns with the common RMS-to-peak relationship for a sine wave, where peak = RMS × sqrt(2). The other numbers don’t fit because they correspond to no offset or different geometric outcomes.