Roots of trigonometric equation $sin((n+1)theta) + 2sin(ntheta) = 0,;;thetaneq kpi,,kinmathbb{Z}.$
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I am trying to find a closed formula for the roots of the following trigonometric equation,
$$sin((n+1)theta) + 2sin(ntheta) = 0,;;thetaneq kpi,,kinmathbb{Z},$$
where $n$ is a positive integer.
Can anyone give me a hint?
calculus real-analysis trigonometry roots
edited Nov 27 at 13:25
KM101
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asked Nov 27 at 13:19
math_lover
9010
add a comment |
up vote
1
down vote
favorite
I am trying to find a closed formula for the roots of the following trigonometric equation,
$$sin((n+1)theta) + 2sin(ntheta) = 0,;;thetaneq kpi,,kinmathbb{Z},$$
where $n$ is a positive integer.
Can anyone give me a hint?
calculus real-analysis trigonometry roots
edited Nov 27 at 13:25
KM101
3,719417
asked Nov 27 at 13:19
math_lover
9010
Looking at $n=2$ and $n=3$ in Wolfram Alpha does not look promising. You can probably reduce the problem to solving a $n$-th degree polynomial for $t=tan(theta/2)$, but a closed formula seems unattainable.
– Olivier Moschetta
Nov 27 at 13:26
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am trying to find a closed formula for the roots of the following trigonometric equation,
$$sin((n+1)theta) + 2sin(ntheta) = 0,;;thetaneq kpi,,kinmathbb{Z},$$
where $n$ is a positive integer.
Can anyone give me a hint?
calculus real-analysis trigonometry roots
edited Nov 27 at 13:25
KM101
3,719417
asked Nov 27 at 13:19
math_lover
9010
I am trying to find a closed formula for the roots of the following trigonometric equation,
$$sin((n+1)theta) + 2sin(ntheta) = 0,;;thetaneq kpi,,kinmathbb{Z},$$
where $n$ is a positive integer.
Can anyone give me a hint?
calculus real-analysis trigonometry roots
calculus real-analysis trigonometry roots
edited Nov 27 at 13:25
KM101
3,719417
asked Nov 27 at 13:19
math_lover
9010
edited Nov 27 at 13:25
KM101
3,719417
asked Nov 27 at 13:19
math_lover
9010
edited Nov 27 at 13:25
KM101
3,719417
edited Nov 27 at 13:25
KM101
3,719417
edited Nov 27 at 13:25
KM101
3,719417
3,719417
asked Nov 27 at 13:19
math_lover
9010
asked Nov 27 at 13:19
math_lover
9010
asked Nov 27 at 13:19
math_lover
9010
9010
Looking at $n=2$ and $n=3$ in Wolfram Alpha does not look promising. You can probably reduce the problem to solving a $n$-th degree polynomial for $t=tan(theta/2)$, but a closed formula seems unattainable.
– Olivier Moschetta
Nov 27 at 13:26
add a comment |
Looking at $n=2$ and $n=3$ in Wolfram Alpha does not look promising. You can probably reduce the problem to solving a $n$-th degree polynomial for $t=tan(theta/2)$, but a closed formula seems unattainable.
– Olivier Moschetta
Nov 27 at 13:26
Looking at $n=2$ and $n=3$ in Wolfram Alpha does not look promising. You can probably reduce the problem to solving a $n$-th degree polynomial for $t=tan(theta/2)$, but a closed formula seems unattainable.
– Olivier Moschetta
Nov 27 at 13:26
Looking at $n=2$ and $n=3$ in Wolfram Alpha does not look promising. You can probably reduce the problem to solving a $n$-th degree polynomial for $t=tan(theta/2)$, but a closed formula seems unattainable.
– Olivier Moschetta
Nov 27 at 13:26
add a comment |
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Looking at $n=2$ and $n=3$ in Wolfram Alpha does not look promising. You can probably reduce the problem to solving a $n$-th degree polynomial for $t=tan(theta/2)$, but a closed formula seems unattainable.
– Olivier Moschetta
Nov 27 at 13:26