What is the Amplitude and Phase Angle of Resultant Waves on the Same String?

[ee1215]

Homework Statement

These two waves travel along the same string:
y1(x,t)=7.00mm*sin(2pi x - 428pi t +0.38pi)
y2(x,t)=6.00mm*sin(2pi x - 428pi t + 0.93pi)
A) amplitude in mm
B) phase angle(relative to wave 1) of resultant wave
C) if third wave of amplitude 7.40mm is also to be sent along the string in same direction as first two, what should be its phase angle in order to maximize the amplitude of the new resultant wave?

Homework Equations

Amplitude would then be sqrt[(veritcal)^2+(horizontal)^2]
Phase angle = tan^-1 (vert/horiz)

The Attempt at a Solution

Need to find horizontal and vertical:
7.00cos(0.38pi)+6.00cos(0.93pi) - horizontal
7.00sin(0.38pi)+6.00sin(0.93pi) - vertical

For horizontal I got 12.98mm and verical 0.452mm but when using the equations I get the incorrect answer so I am doing something wrong with calculating horizontal and vertical.

 

[_coyote_]

For part c, I would just need to use the equations and find the phase angle that maximizes the amplitude but I am stuck at part A and B. Thanks for any help!