cosecant

Like: it's a pretty useless skill to have memorized what the anti-derivative of the cosecant function is.

It always bugged me that secant is 1/cosine, cosecant is 1/sine, and cotangent is 1/tangent.

If you mess up a chain-rule question by misremembering the derivative of the inverse cosecant function, then you should get more questions about the inverse cosecant function rather than the chain rule, and vice versa.

This article (or a comment) mentions the famous cosecant tablet.

The right metaphors are essential; I can now visualize the cosecant, where it'd be useful, and intuit why cot^2 + 1^2 = csc^2.

I have found that the biggest gap is actually understanding what sine, cosine, tangent, secant, cosecant and cotangent are.

The length of the segment from C to the origin will be the cosecant and the segment from the y axis to C will be the cotangent.

I never actually knew the significance of secant and cosecant, or how tangent/cotangents' lengths were related to the unit circle and right triangle.

Similar things happened when I sat down to understand exactly what sine, cosine, tangent, cotangent, secant and cosecant were on a circle.

Trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent are used to calculate the values of angles and sides of triangles.

The simplest example I can think of is something like a math library -- if I have code that computes the cosecant of x, I don't really know if it's working or not.

However, I also had to do what you did with Trigonometry - one of the extremely irritating things is that nobody teaches you why the names are sine, cosine, tangent, cotangent, secant and cosecant.

Then the Calc class was like 70% memorizing "whats the integral of cosecant?", was which I think we should be able to agree is absurdly useless even for people who actively work in a math-heavy field.