Question

Determine the resultant of the two waves E1 = 4.00 sin(100 πt) and E2 = 7.80 sin(100 πt + π/2).
E1 + E2 =

Answer 1

Best Answer:  R = 4.00 sin(100πt) + 7.80sin(100πt + π/2).

Note that for any angle x, cosx = sin(x+π/2) so:
R =4.00 sin(100πt) + 7.80sin(100πt + π/2).

The expression Asin(x) + Bcos(x) can be reduced to Csin(x+φ) where:
C = √(A² + B²) and φ = tan⁻¹(B/A)
This is a standard result you should have been taught. If you do a search on 'Asin(x) + Bcos(x)' you will a full explanation - e.g. see link.

In the expression '4.00sin(100πt) + 7.80cos(100πt)', 'x' corresponds to 100πt. A=4and B=7.8
C = √(A² + B²) = √(4² + 7.8²) = 8.765
φ = tan⁻¹(7.8/4) = 1.95 (remember to switch calculator to radians mode for this and return it to degrees if needed!!!)

R =4.00(8.765 sin(100πt) + 7.80(8.765sin(100πt + 1.95))
R = 35.06sin (100πt)+ 68.36 sin(100πt + 1.95)