Which variants of trig functions are we required to know (knowing how to graph with domains and ranges) for the AQA A-level Further Maths in this summer's exams?

I know we need to be able to recognise, graph, and state domains and ranges for:

- The basic trig functions (sinx, cosx, tanx)

- The reciprocal trig functions (cosechx, sechx, cothx)

- The inverse trig functions (arcsinx, arccosx, arctanx)

- The hyperbolic trig functions (sinhx, coshx, tanhx)

But is it necessary to have the same level of understanding regarding these?:

- The reciprocal hyperbolic functions (cosechx, sechx, cothx)

- The inverse hyperbolic functions (arsinhx, arcosh, artanhx)

- The inverse reciprocal functions (arcosecx, arsecx, arcotx)

And also this one?!:

- The inverse reciprocal hyperbolic functions (arcosechx, arsechx, arcothx)

I hope a deep understanding of all of these is not required but any help in knowing which ones to know would be greatly appreciated!

I know we need to be able to recognise, graph, and state domains and ranges for:

- The basic trig functions (sinx, cosx, tanx)

- The reciprocal trig functions (cosechx, sechx, cothx)

- The inverse trig functions (arcsinx, arccosx, arctanx)

- The hyperbolic trig functions (sinhx, coshx, tanhx)

But is it necessary to have the same level of understanding regarding these?:

- The reciprocal hyperbolic functions (cosechx, sechx, cothx)

- The inverse hyperbolic functions (arsinhx, arcosh, artanhx)

- The inverse reciprocal functions (arcosecx, arsecx, arcotx)

And also this one?!:

- The inverse reciprocal hyperbolic functions (arcosechx, arsechx, arcothx)

I hope a deep understanding of all of these is not required but any help in knowing which ones to know would be greatly appreciated!

Well if you know the graphs to cosh(x) and sec(x) and such, graphing reciprocals and inverses aren't too bad.

So really the only curves to remember are sin, cos, tan, sinh (which looks like x^3), cosh (which looks like x^2+1), and tanh (which looks like arctan, but the range is (-1,1)).

•

Reciprocals are just 1/blah (and construct from here - that's how I remember the graph for sec(x) anyway. Compare the graphs of cos(x) and sec(x) and see if you can get the construction.)

•

Inverses are just mirroring the graph (on a correct domain) along x=y.

So really the only curves to remember are sin, cos, tan, sinh (which looks like x^3), cosh (which looks like x^2+1), and tanh (which looks like arctan, but the range is (-1,1)).

(edited 1 month ago)

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