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Since math is a minimalistic science, what's the idea of defining such a thing like cosecant or secant?...
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This question already has an answer here:
Why do we need so many trigonometric definitions?
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As we all know, math is a minimalistic science. For example we don't put into the definition of differentiable functions that they have to be continuous. So my question is this:
What's the idea of defining such a thing like cosecant or secant? I have never seen their use in math or other science.
geometry trigonometry
edited Jan 31 at 21:46
Blue
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asked Jan 31 at 21:40
LucianLucian
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Jan 31 at 21:47
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Why do we need so many trigonometric definitions?
7 answers
As we all know, math is a minimalistic science. For example we don't put into the definition of differentiable functions that they have to be continuous. So my question is this:
What's the idea of defining such a thing like cosecant or secant? I have never seen their use in math or other science.
geometry trigonometry
edited Jan 31 at 21:46
Blue
49.5k870158
asked Jan 31 at 21:40
LucianLucian
396
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marked as duplicate by Blue geometry
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Jan 31 at 21:47
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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it is a useful notation abbreviation sometimes
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– gt6989b
Jan 31 at 21:44
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It would be interesting to see in which "mathematical geographical areas" sec and cosec are still used. For example, in France, they aren't used, and as far as I know they have never been used.
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– Jean Marie
Feb 1 at 19:53
add a comment |
$begingroup$
This question already has an answer here:
Why do we need so many trigonometric definitions?
7 answers
As we all know, math is a minimalistic science. For example we don't put into the definition of differentiable functions that they have to be continuous. So my question is this:
What's the idea of defining such a thing like cosecant or secant? I have never seen their use in math or other science.
geometry trigonometry
edited Jan 31 at 21:46
Blue
49.5k870158
asked Jan 31 at 21:40
LucianLucian
396
$endgroup$
This question already has an answer here:
Why do we need so many trigonometric definitions?
7 answers
As we all know, math is a minimalistic science. For example we don't put into the definition of differentiable functions that they have to be continuous. So my question is this:
What's the idea of defining such a thing like cosecant or secant? I have never seen their use in math or other science.
This question already has an answer here:
Why do we need so many trigonometric definitions?
7 answers
geometry trigonometry
geometry trigonometry
edited Jan 31 at 21:46
Blue
49.5k870158
asked Jan 31 at 21:40
LucianLucian
396
edited Jan 31 at 21:46
Blue
49.5k870158
asked Jan 31 at 21:40
LucianLucian
396
edited Jan 31 at 21:46
Blue
49.5k870158
edited Jan 31 at 21:46
Blue
49.5k870158
edited Jan 31 at 21:46
Blue
49.5k870158
49.5k870158
asked Jan 31 at 21:40
LucianLucian
396
asked Jan 31 at 21:40
LucianLucian
396
asked Jan 31 at 21:40
LucianLucian
396
396
marked as duplicate by Blue geometry
Users with the geometry badge can single-handedly close geometry questions as duplicates and reopen them as needed.
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Jan 31 at 21:47
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Jan 31 at 21:47
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
it is a useful notation abbreviation sometimes
$endgroup$
– gt6989b
Jan 31 at 21:44
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It would be interesting to see in which "mathematical geographical areas" sec and cosec are still used. For example, in France, they aren't used, and as far as I know they have never been used.
$endgroup$
– Jean Marie
Feb 1 at 19:53
add a comment |
$begingroup$
it is a useful notation abbreviation sometimes
$endgroup$
– gt6989b
Jan 31 at 21:44
$begingroup$
It would be interesting to see in which "mathematical geographical areas" sec and cosec are still used. For example, in France, they aren't used, and as far as I know they have never been used.
$endgroup$
– Jean Marie
Feb 1 at 19:53
$begingroup$
it is a useful notation abbreviation sometimes
$endgroup$
– gt6989b
Jan 31 at 21:44
$begingroup$
it is a useful notation abbreviation sometimes
$endgroup$
– gt6989b
Jan 31 at 21:44
$begingroup$
It would be interesting to see in which "mathematical geographical areas" sec and cosec are still used. For example, in France, they aren't used, and as far as I know they have never been used.
$endgroup$
– Jean Marie
Feb 1 at 19:53
$begingroup$
It would be interesting to see in which "mathematical geographical areas" sec and cosec are still used. For example, in France, they aren't used, and as far as I know they have never been used.
$endgroup$
– Jean Marie
Feb 1 at 19:53
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If you're asking how they are defined then:
$$sec(x) = frac{1}{cos(x)}$$
and $$csc(x) = frac{1}{sin(x)}$$
If you're asking when the are used, almost everything in higher level math or physics relies on some knowledge of trigonometry. For example, when you take a Complex Analysis Class, knowledge of trigonometric functions is heavily used.
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
$endgroup$
6
$begingroup$
I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $frac{1}{cosx}$ and $frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.
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– Mark
Jan 31 at 21:48
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If you're asking how they are defined then:
$$sec(x) = frac{1}{cos(x)}$$
and $$csc(x) = frac{1}{sin(x)}$$
If you're asking when the are used, almost everything in higher level math or physics relies on some knowledge of trigonometry. For example, when you take a Complex Analysis Class, knowledge of trigonometric functions is heavily used.
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
$endgroup$
6
$begingroup$
I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $frac{1}{cosx}$ and $frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.
$endgroup$
– Mark
Jan 31 at 21:48
add a comment |
$begingroup$
If you're asking how they are defined then:
$$sec(x) = frac{1}{cos(x)}$$
and $$csc(x) = frac{1}{sin(x)}$$
If you're asking when the are used, almost everything in higher level math or physics relies on some knowledge of trigonometry. For example, when you take a Complex Analysis Class, knowledge of trigonometric functions is heavily used.
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
$endgroup$
6
$begingroup$
I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $frac{1}{cosx}$ and $frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.
$endgroup$
– Mark
Jan 31 at 21:48
add a comment |
$begingroup$
If you're asking how they are defined then:
$$sec(x) = frac{1}{cos(x)}$$
and $$csc(x) = frac{1}{sin(x)}$$
If you're asking when the are used, almost everything in higher level math or physics relies on some knowledge of trigonometry. For example, when you take a Complex Analysis Class, knowledge of trigonometric functions is heavily used.
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
$endgroup$
If you're asking how they are defined then:
$$sec(x) = frac{1}{cos(x)}$$
and $$csc(x) = frac{1}{sin(x)}$$
If you're asking when the are used, almost everything in higher level math or physics relies on some knowledge of trigonometry. For example, when you take a Complex Analysis Class, knowledge of trigonometric functions is heavily used.
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
answered Jan 31 at 21:45
Aniruddh VenkatesanAniruddh Venkatesan
151113
151113
6
$begingroup$
I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $frac{1}{cosx}$ and $frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.
$endgroup$
– Mark
Jan 31 at 21:48
add a comment |
6
$begingroup$
I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $frac{1}{cosx}$ and $frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.
$endgroup$
– Mark
Jan 31 at 21:48
6
6
$begingroup$
I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $frac{1}{cosx}$ and $frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.
$endgroup$
– Mark
Jan 31 at 21:48
$begingroup$
I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $frac{1}{cosx}$ and $frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.
$endgroup$
– Mark
Jan 31 at 21:48
add a comment |
$begingroup$
it is a useful notation abbreviation sometimes
$endgroup$
– gt6989b
Jan 31 at 21:44
$begingroup$
It would be interesting to see in which "mathematical geographical areas" sec and cosec are still used. For example, in France, they aren't used, and as far as I know they have never been used.
$endgroup$
– Jean Marie
Feb 1 at 19:53