Solving for $z$ in $x=frac y{2 tan(z/2)}$
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I'm trying to solve for $z$ given $x=dfrac y{2 tan(z/2)}$.
Wolfram Alpha gives me the solution, but when I plug the formula into Excel it's not giving expected results at all - if I plug the same $x$ value into the formula it does not give me the $z$ that I originally started with.
Hopefully that's enough information to go off of; normally I frequent Stackoverflow. Thanks!
trigonometry
edited 2 days ago
amWhy
191k27223438
asked 2 days ago
user3763099
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New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
up vote
0
down vote
favorite
I'm trying to solve for $z$ given $x=dfrac y{2 tan(z/2)}$.
Wolfram Alpha gives me the solution, but when I plug the formula into Excel it's not giving expected results at all - if I plug the same $x$ value into the formula it does not give me the $z$ that I originally started with.
Hopefully that's enough information to go off of; normally I frequent Stackoverflow. Thanks!
trigonometry
edited 2 days ago
amWhy
191k27223438
asked 2 days ago
user3763099
1
New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You should not necessarily be surprised to get back a different value of $z$. Instead you should keep an open mind to the possibility that the equation is satisfied by many choices for $z$ even without changing $x$ and $y$. A formula that Excel can use will only produce a single value.
– Jyrki Lahtonen
yesterday
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm trying to solve for $z$ given $x=dfrac y{2 tan(z/2)}$.
Wolfram Alpha gives me the solution, but when I plug the formula into Excel it's not giving expected results at all - if I plug the same $x$ value into the formula it does not give me the $z$ that I originally started with.
Hopefully that's enough information to go off of; normally I frequent Stackoverflow. Thanks!
trigonometry
edited 2 days ago
amWhy
191k27223438
asked 2 days ago
user3763099
1
New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm trying to solve for $z$ given $x=dfrac y{2 tan(z/2)}$.
Wolfram Alpha gives me the solution, but when I plug the formula into Excel it's not giving expected results at all - if I plug the same $x$ value into the formula it does not give me the $z$ that I originally started with.
Hopefully that's enough information to go off of; normally I frequent Stackoverflow. Thanks!
trigonometry
trigonometry
edited 2 days ago
amWhy
191k27223438
asked 2 days ago
user3763099
1
New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
amWhy
191k27223438
asked 2 days ago
user3763099
1
New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
amWhy
191k27223438
edited 2 days ago
amWhy
191k27223438
edited 2 days ago
amWhy
191k27223438
191k27223438
asked 2 days ago
user3763099
1
New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
user3763099
1
asked 2 days ago
user3763099
1
1
New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user3763099 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You should not necessarily be surprised to get back a different value of $z$. Instead you should keep an open mind to the possibility that the equation is satisfied by many choices for $z$ even without changing $x$ and $y$. A formula that Excel can use will only produce a single value.
– Jyrki Lahtonen
yesterday
add a comment |
You should not necessarily be surprised to get back a different value of $z$. Instead you should keep an open mind to the possibility that the equation is satisfied by many choices for $z$ even without changing $x$ and $y$. A formula that Excel can use will only produce a single value.
– Jyrki Lahtonen
yesterday
You should not necessarily be surprised to get back a different value of $z$. Instead you should keep an open mind to the possibility that the equation is satisfied by many choices for $z$ even without changing $x$ and $y$. A formula that Excel can use will only produce a single value.
– Jyrki Lahtonen
yesterday
You should not necessarily be surprised to get back a different value of $z$. Instead you should keep an open mind to the possibility that the equation is satisfied by many choices for $z$ even without changing $x$ and $y$. A formula that Excel can use will only produce a single value.
– Jyrki Lahtonen
yesterday
add a comment |
2 Answers
2
active
oldest
votes
up vote
1
down vote
We have
$$x=frac y {2 tan(z/2)} iff tan(z/2)=frac y {2x} iff z=2arctan frac y {2x}+2kpi$$
provided that $zneq 0 quad xneq 0$.
answered 2 days ago
gimusi
89.1k74495
Where does 'k' come from, how do I find this value?
– user3763099
2 days ago
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
2 days ago
add a comment |
up vote
0
down vote
The solution is
$$2 left(pi c_1+cot ^{-1}left(frac{2 x}{y}right)right)$$
where $c_1$ is an integer.
Doesn't this work for you?
answered 2 days ago
David G. Stork
9,28521232
That's the formula I'm using, but maybe I'm lost as to what integer c1 is supposed to be. To me, this seems like an unsolved value, so I'm frankly confused as to what I should plug in there. Where does this come from?
– user3763099
2 days ago
$c_1$ is any integer value. You probably know that trig functions are periodic. $tan b(x)$ is periodic and repeats every $frac{pi}{b}$ radians. (Every $pi$ radians if $b = 1$.) For example, $tan frac{pi}{4} = tan frac{5pi}{4}$.
– KM101
2 days ago
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
We have
$$x=frac y {2 tan(z/2)} iff tan(z/2)=frac y {2x} iff z=2arctan frac y {2x}+2kpi$$
provided that $zneq 0 quad xneq 0$.
answered 2 days ago
gimusi
89.1k74495
Where does 'k' come from, how do I find this value?
– user3763099
2 days ago
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
2 days ago
add a comment |
up vote
1
down vote
We have
$$x=frac y {2 tan(z/2)} iff tan(z/2)=frac y {2x} iff z=2arctan frac y {2x}+2kpi$$
provided that $zneq 0 quad xneq 0$.
answered 2 days ago
gimusi
89.1k74495
Where does 'k' come from, how do I find this value?
– user3763099
2 days ago
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
2 days ago
add a comment |
up vote
1
down vote
up vote
1
down vote
We have
$$x=frac y {2 tan(z/2)} iff tan(z/2)=frac y {2x} iff z=2arctan frac y {2x}+2kpi$$
provided that $zneq 0 quad xneq 0$.
answered 2 days ago
gimusi
89.1k74495
We have
$$x=frac y {2 tan(z/2)} iff tan(z/2)=frac y {2x} iff z=2arctan frac y {2x}+2kpi$$
provided that $zneq 0 quad xneq 0$.
answered 2 days ago
gimusi
89.1k74495
answered 2 days ago
gimusi
89.1k74495
answered 2 days ago
gimusi
89.1k74495
answered 2 days ago
gimusi
89.1k74495
89.1k74495
Where does 'k' come from, how do I find this value?
– user3763099
2 days ago
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
2 days ago
add a comment |
Where does 'k' come from, how do I find this value?
– user3763099
2 days ago
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
2 days ago
Where does 'k' come from, how do I find this value?
– user3763099
2 days ago
Where does 'k' come from, how do I find this value?
– user3763099
2 days ago
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
2 days ago
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
2 days ago
add a comment |
up vote
0
down vote
The solution is
$$2 left(pi c_1+cot ^{-1}left(frac{2 x}{y}right)right)$$
where $c_1$ is an integer.
Doesn't this work for you?
answered 2 days ago
David G. Stork
9,28521232
That's the formula I'm using, but maybe I'm lost as to what integer c1 is supposed to be. To me, this seems like an unsolved value, so I'm frankly confused as to what I should plug in there. Where does this come from?
– user3763099
2 days ago
$c_1$ is any integer value. You probably know that trig functions are periodic. $tan b(x)$ is periodic and repeats every $frac{pi}{b}$ radians. (Every $pi$ radians if $b = 1$.) For example, $tan frac{pi}{4} = tan frac{5pi}{4}$.
– KM101
2 days ago
add a comment |
up vote
0
down vote
The solution is
$$2 left(pi c_1+cot ^{-1}left(frac{2 x}{y}right)right)$$
where $c_1$ is an integer.
Doesn't this work for you?
answered 2 days ago
David G. Stork
9,28521232
That's the formula I'm using, but maybe I'm lost as to what integer c1 is supposed to be. To me, this seems like an unsolved value, so I'm frankly confused as to what I should plug in there. Where does this come from?
– user3763099
2 days ago
$c_1$ is any integer value. You probably know that trig functions are periodic. $tan b(x)$ is periodic and repeats every $frac{pi}{b}$ radians. (Every $pi$ radians if $b = 1$.) For example, $tan frac{pi}{4} = tan frac{5pi}{4}$.
– KM101
2 days ago
add a comment |
up vote
0
down vote
up vote
0
down vote
The solution is
$$2 left(pi c_1+cot ^{-1}left(frac{2 x}{y}right)right)$$
where $c_1$ is an integer.
Doesn't this work for you?
answered 2 days ago
David G. Stork
9,28521232
The solution is
$$2 left(pi c_1+cot ^{-1}left(frac{2 x}{y}right)right)$$
where $c_1$ is an integer.
Doesn't this work for you?
answered 2 days ago
David G. Stork
9,28521232
answered 2 days ago
David G. Stork
9,28521232
answered 2 days ago
David G. Stork
9,28521232
answered 2 days ago
David G. Stork
9,28521232
9,28521232
That's the formula I'm using, but maybe I'm lost as to what integer c1 is supposed to be. To me, this seems like an unsolved value, so I'm frankly confused as to what I should plug in there. Where does this come from?
– user3763099
2 days ago
$c_1$ is any integer value. You probably know that trig functions are periodic. $tan b(x)$ is periodic and repeats every $frac{pi}{b}$ radians. (Every $pi$ radians if $b = 1$.) For example, $tan frac{pi}{4} = tan frac{5pi}{4}$.
– KM101
2 days ago
add a comment |
That's the formula I'm using, but maybe I'm lost as to what integer c1 is supposed to be. To me, this seems like an unsolved value, so I'm frankly confused as to what I should plug in there. Where does this come from?
– user3763099
2 days ago
$c_1$ is any integer value. You probably know that trig functions are periodic. $tan b(x)$ is periodic and repeats every $frac{pi}{b}$ radians. (Every $pi$ radians if $b = 1$.) For example, $tan frac{pi}{4} = tan frac{5pi}{4}$.
– KM101
2 days ago
That's the formula I'm using, but maybe I'm lost as to what integer c1 is supposed to be. To me, this seems like an unsolved value, so I'm frankly confused as to what I should plug in there. Where does this come from?
– user3763099
2 days ago
That's the formula I'm using, but maybe I'm lost as to what integer c1 is supposed to be. To me, this seems like an unsolved value, so I'm frankly confused as to what I should plug in there. Where does this come from?
– user3763099
2 days ago
$c_1$ is any integer value. You probably know that trig functions are periodic. $tan b(x)$ is periodic and repeats every $frac{pi}{b}$ radians. (Every $pi$ radians if $b = 1$.) For example, $tan frac{pi}{4} = tan frac{5pi}{4}$.
– KM101
2 days ago
$c_1$ is any integer value. You probably know that trig functions are periodic. $tan b(x)$ is periodic and repeats every $frac{pi}{b}$ radians. (Every $pi$ radians if $b = 1$.) For example, $tan frac{pi}{4} = tan frac{5pi}{4}$.
– KM101
2 days ago
add a comment |
user3763099 is a new contributor. Be nice, and check out our Code of Conduct.
user3763099 is a new contributor. Be nice, and check out our Code of Conduct.
user3763099 is a new contributor. Be nice, and check out our Code of Conduct.
user3763099 is a new contributor. Be nice, and check out our Code of Conduct.
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You should not necessarily be surprised to get back a different value of $z$. Instead you should keep an open mind to the possibility that the equation is satisfied by many choices for $z$ even without changing $x$ and $y$. A formula that Excel can use will only produce a single value.
– Jyrki Lahtonen
yesterday