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Can y(x)=a*sin(kx)+b*cos(kx) presented simpler?

  1. Apr 3, 2004 #1
    Hi!

    i wonder if it's possible to present y(x)=a*sin(kx)+b*cos(kx) as one function like y(x)=A*sin(kx+c) where A and c are constants?
     
  2. jcsd
  3. Apr 3, 2004 #2

    Hurkyl

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    Sure is. Try using the addition of angle formula on A*sin(kx+c) and see if you can figure out how!
     
  4. Apr 3, 2004 #3
    substitue [tex]a= \sqrt{a^2+b^2} * cos \theta[/tex]
    and [tex] b= \sqrt{a^2+b^2} * sin \theta[/tex]

    now
    u can see that

    A= [tex]\sqrt{a^2+b^2} [/tex]

    and c= [tex]\theta = \arctan {\frac{b}{a}}[/tex]
     
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