* How to simplify "sin(x)^2 + cos(x)^2" to 1 in calc?
@ 2023-06-09 4:48 Vladimir Nikishkin
2023-06-10 0:02 ` Michael Heerdegen
2023-06-11 3:07 ` Michael Heerdegen
0 siblings, 2 replies; 3+ messages in thread
From: Vladimir Nikishkin @ 2023-06-09 4:48 UTC (permalink / raw)
To: help-gnu-emacs
Hello, everyone.
Please, refer me to a correct mailing list if this one is not
appropriate,
I am trying to make calc apply the most basic trigonometric identity,
and simplify the algebraic formula "sin(x)^2 + cos(x)^2" to 1.
I tried 'a v', 'a "', '=', 'j D', 'j M', but seemingly, all in vain,
even though "sin(x)^2 + cos(x)^2 = 1" seems to be one of the safest
substitutions in algebra. (Not sure about 'x having a quaternion value,
or working in some arithmetic mod p.)
What am I doing wrong?
--
Your sincerely,
Vladimir Nikishkin (MiEr, lockywolf)
(Laptop)
^ permalink raw reply [flat|nested] 3+ messages in thread
* Re: How to simplify "sin(x)^2 + cos(x)^2" to 1 in calc?
2023-06-09 4:48 How to simplify "sin(x)^2 + cos(x)^2" to 1 in calc? Vladimir Nikishkin
@ 2023-06-10 0:02 ` Michael Heerdegen
2023-06-11 3:07 ` Michael Heerdegen
1 sibling, 0 replies; 3+ messages in thread
From: Michael Heerdegen @ 2023-06-10 0:02 UTC (permalink / raw)
To: help-gnu-emacs
Vladimir Nikishkin <lockywolf@gmail.com> writes:
> Hello, everyone.
>
> Please, refer me to a correct mailing list if this one is not
> appropriate,
This one is good.
> I am trying to make calc apply the most basic trigonometric identity,
> and simplify the algebraic formula "sin(x)^2 + cos(x)^2" to 1.
>
> I tried 'a v', 'a "', '=', 'j D', 'j M', but seemingly, all in vain,
> even though "sin(x)^2 + cos(x)^2 = 1" seems to be one of the safest
> substitutions in algebra. (Not sure about 'x having a quaternion value,
> or working in some arithmetic mod p.)
>
> What am I doing wrong?
Nothing, I guess. It's indeed surprising that Calc fails to perform
this simplification automatically.
This identity is discussed in several places in the Calc manual. With
the extended algebraic simplification mode enabled, Calc even simplifies
sqrt(1 - sin(x)^2) to cos(x). But not 1 - sin(x)^2 to cos(x)^2 or
sin(x)^2+cos(x)^2 to 1.
Seems to be a known limitation though: the chapters about rewrite rules
talk about how to apply the Pythagorean trigonometric identity manually.
It seems you have to force the application in most situations.
Calc's automatic rewrite and simplification capabilities are sometimes a
bit limited.
Michael.
^ permalink raw reply [flat|nested] 3+ messages in thread
* Re: How to simplify "sin(x)^2 + cos(x)^2" to 1 in calc?
2023-06-09 4:48 How to simplify "sin(x)^2 + cos(x)^2" to 1 in calc? Vladimir Nikishkin
2023-06-10 0:02 ` Michael Heerdegen
@ 2023-06-11 3:07 ` Michael Heerdegen
1 sibling, 0 replies; 3+ messages in thread
From: Michael Heerdegen @ 2023-06-11 3:07 UTC (permalink / raw)
To: Vladimir Nikishkin; +Cc: help-gnu-emacs
Vladimir Nikishkin <lockywolf@gmail.com> writes:
> Hello, everyone.
>
> Please, refer me to a correct mailing list if this one is not
> appropriate,
This one is good.
> I am trying to make calc apply the most basic trigonometric identity,
> and simplify the algebraic formula "sin(x)^2 + cos(x)^2" to 1.
>
> I tried 'a v', 'a "', '=', 'j D', 'j M', but seemingly, all in vain,
> even though "sin(x)^2 + cos(x)^2 = 1" seems to be one of the safest
> substitutions in algebra. (Not sure about 'x having a quaternion value,
> or working in some arithmetic mod p.)
>
> What am I doing wrong?
Nothing, I guess. It's indeed surprising that Calc fails to perform
this simplification automatically.
This identity is discussed in several places in the Calc manual. With
the extended algebraic simplification mode enabled, Calc even simplifies
sqrt(1 - sin(x)^2) to cos(x). But not 1 - sin(x)^2 to cos(x)^2 or
sin(x)^2+cos(x)^2 to 1.
Seems to be a known limitation though: the chapters about rewrite rules
talk about how to apply the Pythagorean trigonometric identity manually.
It seems you have to force the application in most situations.
Calc's automatic rewrite and simplification capabilities are sometimes a
bit limited.
Michael.
^ permalink raw reply [flat|nested] 3+ messages in thread
end of thread, other threads:[~2023-06-11 3:07 UTC | newest]
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2023-06-09 4:48 How to simplify "sin(x)^2 + cos(x)^2" to 1 in calc? Vladimir Nikishkin
2023-06-10 0:02 ` Michael Heerdegen
2023-06-11 3:07 ` Michael Heerdegen
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