Say I have a cos function, $y = 1.2cos(0.503x) + 5$ And say I want to replicate it using sine, so expressing the above function in sine so that it gives "the same wave".

How would I do this? I know I have to find a phase shift, but I don't get the steps on how to do it. Also, please no use of Wolframalpha or the like, because I'll have to do these types of problems in class without them.

Thank you in advance.

  • $\begingroup$ do you just want $1.2\cos(0.503x + \pi/2) + 5 = 1.2\sin(0.503(x + \pi/(2*.503)) + 5?$ $\endgroup$ – abel Jun 7 '15 at 2:34
  • $\begingroup$ Not sure what you mean... $\endgroup$ – user164403 Jun 7 '15 at 2:36
  • $\begingroup$ Yes, that is what I want. $\endgroup$ – user164403 Jun 7 '15 at 2:40


$\cos(x)$ is $\sin(x)$ shifted by $\pi/2$

$$\therefore \sin(x) = \cos(x - \pi/2)$$

  • $\begingroup$ I see. So heres what I got from that: Since period is 2p/|k| = 2pi / 0.5 which is approx 4pi, and there is a (pi/2) shift between cos and sin, (pi/2) is a fourth of the period 4pi that I have. Therefore, I'd be shifting approx. 12.5/4, and my equation would be 1.2sin(0.503(x+12.5/4)) + 5? $\endgroup$ – user164403 Jun 7 '15 at 2:31
  • $\begingroup$ @user164403: Try graphing it on WolframAlpha to verify. $\endgroup$ – user174622 Jun 7 '15 at 2:34
  • $\begingroup$ They line up and do in fact work. Thank you for your help. $\endgroup$ – user164403 Jun 7 '15 at 2:36
  • $\begingroup$ @user164403 Then you're done. $\endgroup$ – user174622 Jun 7 '15 at 2:41

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