What is the multiplier for a 30 degree offset?

What is the multiplier for a 30 degree offset?

• A. 3
• B. 4
• C. 2
• D. 1

Answer: (C)

When a quantity is offset by an angle, the portion you measure along a reference axis is reduced by the sine of that offset. To recover the full magnitude from that measured projection, you multiply by the reciprocal of sine, which is the cosecant. For a 30-degree offset, sin(30°) equals 0.5, so the projection is half the total magnitude and the multiplier to get back to the full magnitude is 1/0.5 = 2. This is why the multiplier is two. In phasor or power calculations, you’ll encounter this cosecant relationship whenever you need to translate a projected component back to the total magnitude. The other values would correspond to different offsets, not 30 degrees.

When a quantity is offset by an angle, the portion you measure along a reference axis is reduced by the sine of that offset. To recover the full magnitude from that measured projection, you multiply by the reciprocal of sine, which is the cosecant. For a 30-degree offset, sin(30°) equals 0.5, so the projection is half the total magnitude and the multiplier to get back to the full magnitude is 1/0.5 = 2. This is why the multiplier is two. In phasor or power calculations, you’ll encounter this cosecant relationship whenever you need to translate a projected component back to the total magnitude. The other values would correspond to different offsets, not 30 degrees.