For a math assessment we need to make a identical graph of $3\cos(4x)−5$ using $\sin$ instead of $\cos$? Wondering if anyone can find a formula using $\sin$?

  • 3
    $\begingroup$ $\sin(x) = \cos(x - \frac{\pi}{2})$ $\endgroup$
    – alkabary
    Commented Jun 3, 2015 at 1:57
  • $\begingroup$ Please do not delete your question as it might be useful for others, and you have an accepted answer already. $\endgroup$
    – user99914
    Commented Jun 3, 2015 at 8:48

1 Answer 1


$\sin(x) = \cos(x - \frac{\pi}{2})$ and so $\cos(x) = \sin(x + \frac{\pi}{2})$ and so $$3\cos(4x) - 5 = 3\sin(4x + \frac{\pi}{2})-5$$

Visually $\sin(x) = \cos(x - \frac{\pi}{2})$ means that $\sin$ graph is obtained by just shifting the graph of $\cos$ by $\frac{\pi}{2}$ to the right.


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