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 The cosecant, secant and cotangent functions
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The cosecant, secant and cotangent functions
01212017 06:46 PM
Hi,
Can someone please help me with the following question.
I would like to know how to input the cosecant, secant and cotangent functions and graph them using the HP Prime Graphing Calculator.
Is there a function, like there is for sin, cos and tan, for cosec, sec and cot or do I have to input them using the functions sin and cos?
Regards,
Athanasios
Solved! Go to Solution.
01212017 07:30 PM  edited 01222017 05:03 AM
Hi!, @Athanasios:
You can see the User Guide, for explanation's, from ... http://support.hp.com/usen/product/hpprimegraphingcalculator/5367459/manuals
See too ... http://en.hpprime.club/docs/reference/
Description
Example
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
01212017 08:28 PM
Yes. They are CSC, SEC, and COT, respectively. Their inverse functions are ACSC, ASEC, and ACOT, respectively.
These functions (and all the other ones) can be found easily by using the search function in the calculator's builtin Help facility (click the Help key then tap the Tree button then tap Search), or by searching the HP Prime User Guide (in the Virtual Calculator, click on Help to see it).
Disclaimer: I don't work for HP. I'm just another happy HP calculator user.
05022019 03:03 PM
The only problem with ACOT graph is that it is incorrect. The calculator is using ATAN (1/x) to find values and the graph. However, the negative values of x should return Quadrant II angles (or values between π/2 and π). The calculator does not. If HP is going to program a function, they need to program it to work correctly.
05042019 01:17 AM  edited 05042019 01:18 AM
Hello,
It is correct. The issue is that there are at least 3 possible ways of defining that function  all of which are mathematically valid but behave in different ways. It is actually a rather interesting topic. I believe the HP one functions best when extended into the complex plane, which is why it was chosen.
From: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
(Note: Some authors define the range of arcsecant to be ( 0 ≤ y < π/2 or π ≤ y < 3π/2 ), because the tangent function is nonnegative on this domain. This makes some computations more consistent. For example using this range, tan(arcsec(x)) = sqrtx2 − 1, whereas with the range ( 0 ≤ y < π/2 or π/2 < y ≤ π ), we would have to write tan(arcsec(x)) = ±sqrtx2 − 1, since tangent is nonnegative on 0 ≤ y < π/2 but nonpositive on π/2 < y ≤ π. For a similar reason, the same authors define the range of arccosecant to be −π < y ≤ −π/2 or 0 < y ≤ π/2.)
If x is allowed to be a complex number, then the range of y applies only to its real part.
Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.
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