What is the purpose, if any, of secant, cosecant, and cotangent? I’m an engineering student so I use sine, cosine, and tangent a lot, but almost never the other 3. Creating a new trig function just to be the reciprocal seems to be a bit redundant.
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On a polar plot, cosecant and secant give you horizontal and vertical lines respectively. These can be derived from the basic definition of vertical and horizontal lines, namely that x=c1 or y=c2 for some choice of constants. I’m not sure in how many scenarios you would need to plot straight lines on polar graphs, but the method is there.
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