Solving for $z$ in $x=frac y{2 tan(z/2)}$
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 Nov 30 at 20:11
amWhy
191k28224439
asked Nov 30 at 18:54
user3763099
1
add a comment |
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 Nov 30 at 20:11
amWhy
191k28224439
asked Nov 30 at 18:54
user3763099
1
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
Dec 2 at 6:25
add a comment |
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 Nov 30 at 20:11
amWhy
191k28224439
asked Nov 30 at 18:54
user3763099
1
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 Nov 30 at 20:11
amWhy
191k28224439
asked Nov 30 at 18:54
user3763099
1
edited Nov 30 at 20:11
amWhy
191k28224439
asked Nov 30 at 18:54
user3763099
1
edited Nov 30 at 20:11
amWhy
191k28224439
edited Nov 30 at 20:11
amWhy
191k28224439
edited Nov 30 at 20:11
amWhy
191k28224439
191k28224439
asked Nov 30 at 18:54
user3763099
1
asked Nov 30 at 18:54
user3763099
1
asked Nov 30 at 18:54
user3763099
1
1
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
Dec 2 at 6:25
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
Dec 2 at 6:25
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
Dec 2 at 6:25
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
Dec 2 at 6:25
add a comment |
2 Answers
2
active
oldest
votes
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 Nov 30 at 19:41
gimusi
1
Where does 'k' come from, how do I find this value?
– user3763099
Nov 30 at 19:47
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
Nov 30 at 19:49
add a comment |
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 Nov 30 at 18:58
David G. Stork
9,77921232
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
Nov 30 at 19:40
$c_1$ 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
Nov 30 at 20:21
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 Nov 30 at 19:41
gimusi
1
Where does 'k' come from, how do I find this value?
– user3763099
Nov 30 at 19:47
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
Nov 30 at 19:49
add a comment |
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 Nov 30 at 19:41
gimusi
1
Where does 'k' come from, how do I find this value?
– user3763099
Nov 30 at 19:47
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
Nov 30 at 19:49
add a comment |
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 Nov 30 at 19:41
gimusi
1
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 Nov 30 at 19:41
gimusi
1
answered Nov 30 at 19:41
gimusi
1
answered Nov 30 at 19:41
gimusi
1
answered Nov 30 at 19:41
gimusi
1
1
Where does 'k' come from, how do I find this value?
– user3763099
Nov 30 at 19:47
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
Nov 30 at 19:49
add a comment |
Where does 'k' come from, how do I find this value?
– user3763099
Nov 30 at 19:47
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
Nov 30 at 19:49
Where does 'k' come from, how do I find this value?
– user3763099
Nov 30 at 19:47
Where does 'k' come from, how do I find this value?
– user3763099
Nov 30 at 19:47
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
Nov 30 at 19:49
@user3763099 For example $tan x = 1 implies x=arctan (1)+kpi =pi/4+kpi quad kin mathbb{Z}$
– gimusi
Nov 30 at 19:49
add a comment |
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 Nov 30 at 18:58
David G. Stork
9,77921232
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
Nov 30 at 19:40
$c_1$ 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
Nov 30 at 20:21
add a comment |
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 Nov 30 at 18:58
David G. Stork
9,77921232
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
Nov 30 at 19:40
$c_1$ 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
Nov 30 at 20:21
add a comment |
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 Nov 30 at 18:58
David G. Stork
9,77921232
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 Nov 30 at 18:58
David G. Stork
9,77921232
answered Nov 30 at 18:58
David G. Stork
9,77921232
answered Nov 30 at 18:58
David G. Stork
9,77921232
answered Nov 30 at 18:58
David G. Stork
9,77921232
9,77921232
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
Nov 30 at 19:40
$c_1$ 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
Nov 30 at 20:21
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
Nov 30 at 19:40
$c_1$ 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
Nov 30 at 20:21
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
Nov 30 at 19:40
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
Nov 30 at 19:40
$c_1$ 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
Nov 30 at 20:21
$c_1$ 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
Nov 30 at 20:21
add a comment |
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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
Dec 2 at 6:25