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# The cosecant, secant and cotangent functions

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Hi,

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

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Hi!, @Athanasios:

You can see the User Guide, for explanation's, from ... http://support.hp.com/us-en/product/hp-prime-graphing-calculator/5367459/manuals

See too ... http://en.hpprime.club/docs/reference/

CSC(value)

Description

Cosecant. The Cosecant function; that is, 1/sin(x)

Example

CSC(90) returns 0 in degree mode

ACSC(value)
Description
Arc cosecant. The function derived from the inverse of the Cosecant function.
Example
ACSC(1) returns 90 in degree mode

SEC(value)
Description
Secant. The Secant function; that is, 1/cos(x).
Example
SEC(0) returns 1 in degree mode

ASEC(value)
Description
Arc secant. The function derived from the inverse of the Secant function.
Example
ASEC(1) returns 0 in degree mode

COT(value)
Description
Cotangent. The Cotangent function; that is, cos(x)/sin(x).
Example
COT(45) returns 1 in degree mode

ACOT(value)
Description
Arc cotangent. The function derived from the inverse of the Cotangent function.
Example
ACOT(1) returns 45 in degree mode

Example with plot in radians: ACOT(X)

Kind Regards !.
Have a nice day !.
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
Level 8
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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 built-in 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.

-Joe-
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Thank you Make.

Athanasios

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Thank you Joe Horn.

Athanasios

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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.

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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.

(Note: Some authors define the range of arcsecant to be ( 0 ≤ y < π/2 or πy < 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 < yπ ), we would have to write tan(arcsec(x)) = ±sqrtx2 − 1, since tangent is nonnegative on 0 ≤ y < π/2 but nonpositive on π/2 < yπ. For a similar reason, the same authors define the range of arccosecant to be −π < y ≤ −π/2 or 0 < yπ/2.)

If x is allowed to be a complex number, then the range of y applies only to its real part.

TW

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.
† The opinions expressed above are the personal opinions of the authors, not of HP. By using this site, you accept the Terms of Use and Rules of Participation