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The job that the $\pm$ symbol does is denoting two expressions that differ only in the sign of the summand following the $\pm$. For example, $$b\pm a$$ denotes both $b+a$ and $b-a$ compactly. I am wondering if a common notation exists for the sine and cosine: a notation that compactly represents two expressions that differ only in the trig function, but not the argument.

Brandon Myers
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    I am not familiar with one. It seems natural to write (co)sine. As the cosine and sine functions are the same but shifted by $\frac {\pi}2$ it is common to absorb it into a phase, so $\cos (\omega t + \phi)$ can represent $\sin(\omega t)$ as well with $\phi=\frac \pi 2$ – Ross Millikan Oct 16 '18 at 04:35
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    $\sin(x+(\pi/4)\pm(\pi/4))$. – Gerry Myerson Oct 16 '18 at 06:04
  • $\sin \Bigr[\frac {\pi}4\pm\big(\frac {\pi}4-x\big)\Bigr]?$ I don't know about the argument though... – For the love of maths Oct 16 '18 at 06:04

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