Solving for $z$ in $x=frac y{2 tan(z/2)}$












0












$begingroup$


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







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$endgroup$












  • $begingroup$
    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.
    $endgroup$
    – Jyrki Lahtonen
    Dec 2 '18 at 6:25
















0












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    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.
    $endgroup$
    – Jyrki Lahtonen
    Dec 2 '18 at 6:25














0












0








0


1



$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 30 '18 at 20:11









amWhy

192k28225439




192k28225439










asked Nov 30 '18 at 18:54









user3763099user3763099

1




1












  • $begingroup$
    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.
    $endgroup$
    – Jyrki Lahtonen
    Dec 2 '18 at 6:25


















  • $begingroup$
    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.
    $endgroup$
    – Jyrki Lahtonen
    Dec 2 '18 at 6:25
















$begingroup$
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.
$endgroup$
– Jyrki Lahtonen
Dec 2 '18 at 6:25




$begingroup$
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.
$endgroup$
– Jyrki Lahtonen
Dec 2 '18 at 6:25










2 Answers
2






active

oldest

votes


















1












$begingroup$

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 $zneq 0 quad xneq 0$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Where does 'k' come from, how do I find this value?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:47










  • $begingroup$
    @user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
    $endgroup$
    – gimusi
    Nov 30 '18 at 19:49





















0












$begingroup$

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?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    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?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:40












  • $begingroup$
    $c_1$ 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, $tan frac{pi}{4} = tan frac{5pi}{4}$.
    $endgroup$
    – KM101
    Nov 30 '18 at 20:21













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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

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 $zneq 0 quad xneq 0$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Where does 'k' come from, how do I find this value?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:47










  • $begingroup$
    @user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
    $endgroup$
    – gimusi
    Nov 30 '18 at 19:49


















1












$begingroup$

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 $zneq 0 quad xneq 0$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Where does 'k' come from, how do I find this value?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:47










  • $begingroup$
    @user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
    $endgroup$
    – gimusi
    Nov 30 '18 at 19:49
















1












1








1





$begingroup$

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 $zneq 0 quad xneq 0$.






share|cite|improve this answer









$endgroup$



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 $zneq 0 quad xneq 0$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 30 '18 at 19:41









gimusigimusi

1




1












  • $begingroup$
    Where does 'k' come from, how do I find this value?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:47










  • $begingroup$
    @user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
    $endgroup$
    – gimusi
    Nov 30 '18 at 19:49




















  • $begingroup$
    Where does 'k' come from, how do I find this value?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:47










  • $begingroup$
    @user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
    $endgroup$
    – gimusi
    Nov 30 '18 at 19:49


















$begingroup$
Where does 'k' come from, how do I find this value?
$endgroup$
– user3763099
Nov 30 '18 at 19:47




$begingroup$
Where does 'k' come from, how do I find this value?
$endgroup$
– user3763099
Nov 30 '18 at 19:47












$begingroup$
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
$endgroup$
– gimusi
Nov 30 '18 at 19:49






$begingroup$
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
$endgroup$
– gimusi
Nov 30 '18 at 19:49













0












$begingroup$

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?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    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?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:40












  • $begingroup$
    $c_1$ 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, $tan frac{pi}{4} = tan frac{5pi}{4}$.
    $endgroup$
    – KM101
    Nov 30 '18 at 20:21


















0












$begingroup$

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?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    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?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:40












  • $begingroup$
    $c_1$ 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, $tan frac{pi}{4} = tan frac{5pi}{4}$.
    $endgroup$
    – KM101
    Nov 30 '18 at 20:21
















0












0








0





$begingroup$

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?






share|cite|improve this answer









$endgroup$



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?







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 30 '18 at 18:58









David G. StorkDavid G. Stork

10.2k21332




10.2k21332












  • $begingroup$
    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?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:40












  • $begingroup$
    $c_1$ 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, $tan frac{pi}{4} = tan frac{5pi}{4}$.
    $endgroup$
    – KM101
    Nov 30 '18 at 20:21




















  • $begingroup$
    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?
    $endgroup$
    – user3763099
    Nov 30 '18 at 19:40












  • $begingroup$
    $c_1$ 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, $tan frac{pi}{4} = tan frac{5pi}{4}$.
    $endgroup$
    – KM101
    Nov 30 '18 at 20:21


















$begingroup$
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?
$endgroup$
– user3763099
Nov 30 '18 at 19:40






$begingroup$
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?
$endgroup$
– user3763099
Nov 30 '18 at 19:40














$begingroup$
$c_1$ 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, $tan frac{pi}{4} = tan frac{5pi}{4}$.
$endgroup$
– KM101
Nov 30 '18 at 20:21






$begingroup$
$c_1$ 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, $tan frac{pi}{4} = tan frac{5pi}{4}$.
$endgroup$
– KM101
Nov 30 '18 at 20:21




















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