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March 26th, 2014, 01:08 PM  #1 
Newbie Joined: Mar 2014 Posts: 3 Thanks: 0  Adding Sin waves
I have been tasked with finding the maximum voltage or radius (R) from the sum of two sine waves. (angle written as $) V1=100sin(300t) V2=150cos (300t) Using R sin (wt + $) = a cos(wt) + bsin (wt) then putting in the values taken from above it becomes R sin (300t + $) = 150cos(300t) +100sin(300t) so then R= ?a^2 + b^2 > R= ?150^2 + 100^2 R=180 My question is how does this change if both V1 and V2 use a sin function isstead of the 1 cos and 1 sin function used in the example above? Thankyou 
March 26th, 2014, 01:14 PM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Adding Sin waves
You mean if: V1 = 100sin(100t) V2 = 150sin(100t) Then V1 + V2 = 250sin(100t), which has a max of 250. 
March 26th, 2014, 01:46 PM  #3 
Newbie Joined: Mar 2014 Posts: 3 Thanks: 0  Re: Adding Sin waves
Sorry, I got that wrong. Not the maximum voltage, but the length of the maximum phase angle or Radius. (In my two graphs, there is also a phase shift, so the maximum is not simply the two indices added together.)

March 26th, 2014, 01:56 PM  #4 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Adding Sin waves
What sine functions are you trying to add?

March 26th, 2014, 03:10 PM  #5 
Newbie Joined: Mar 2014 Posts: 3 Thanks: 0  Re: Adding Sin waves
v1 = 20sin(100?t + 2?/5) v2= 35sin(100?t + 2?/9) 
March 26th, 2014, 06:34 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,663 Thanks: 2643 Math Focus: Mainly analysis and algebra  Re: Adding Sin waves
v1 = 20sin(100?t + 2?/5) = 20(sin(100?t)cos(2?/5) + cos(100?t)sin(2?/5)) = (20cos(2?/5)sin(100?t) + 20sin(2?/5)cos(100?t) v2 = 35sin(100?t + 2?/9) = 35cos(2?/9)sin(100?t) + 35sin(2?/9)cos(100?t) v1 + v2 = (20cos(2?/5) + 35cos(2?/9))sin(100?t) + (20sin(2?/5) + 35sin(2?/9))cos(100?t) And you are back to your original sort of equation. 

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