Solving $sin x = 0$, I get $x=ktimes 360^circ$ and $x=ktimes 360^circ+180^circ$, but the answer is $x=ktimes...
How to prove that $sin x = 0$ when $x = ktimes180^circ$?
I tried doing it, but I got these results:
$$x=ktimes 360^circ qquad x=ktimes 360^circ+180^circ$$
trigonometry
edited Oct 30 '18 at 17:28
Blue
47.7k870151
asked Oct 30 '18 at 17:06
LydsLyds
163
add a comment |
How to prove that $sin x = 0$ when $x = ktimes180^circ$?
I tried doing it, but I got these results:
$$x=ktimes 360^circ qquad x=ktimes 360^circ+180^circ$$
trigonometry
edited Oct 30 '18 at 17:28
Blue
47.7k870151
asked Oct 30 '18 at 17:06
LydsLyds
163
Those two answers can be “compressed” into one: $x = pi n$.
– KM101
Oct 30 '18 at 17:11
For one way to "see" what @KM101 said, try writing out all values that $k times 180$ represent in one list, and all values that $k times 360 + 180$ represent in another list, and then make a combined list of everything that shows up in at least one of the first two lists. Make sure you include negative integer values of $k$ when you do this. (Ah ... I see that KM101 was in the middle of doing eactly this when I was writing my comment!)
– Dave L. Renfro
Oct 30 '18 at 17:19
@KM101 how exactly?
– Lyds
Oct 30 '18 at 17:20
Yeah, I’ve added a rather brief explanation with the list. The idea can be applied in both degrees and radians.
– KM101
Oct 30 '18 at 17:20
Check my answer.
– KM101
Oct 30 '18 at 17:20
add a comment |
How to prove that $sin x = 0$ when $x = ktimes180^circ$?
I tried doing it, but I got these results:
$$x=ktimes 360^circ qquad x=ktimes 360^circ+180^circ$$
trigonometry
edited Oct 30 '18 at 17:28
Blue
47.7k870151
asked Oct 30 '18 at 17:06
LydsLyds
163
How to prove that $sin x = 0$ when $x = ktimes180^circ$?
I tried doing it, but I got these results:
$$x=ktimes 360^circ qquad x=ktimes 360^circ+180^circ$$
trigonometry
trigonometry
edited Oct 30 '18 at 17:28
Blue
47.7k870151
asked Oct 30 '18 at 17:06
LydsLyds
163
edited Oct 30 '18 at 17:28
Blue
47.7k870151
asked Oct 30 '18 at 17:06
LydsLyds
163
edited Oct 30 '18 at 17:28
Blue
47.7k870151
edited Oct 30 '18 at 17:28
Blue
47.7k870151
edited Oct 30 '18 at 17:28
Blue
47.7k870151
47.7k870151
asked Oct 30 '18 at 17:06
LydsLyds
163
asked Oct 30 '18 at 17:06
LydsLyds
163
asked Oct 30 '18 at 17:06
LydsLyds
163
163
Those two answers can be “compressed” into one: $x = pi n$.
– KM101
Oct 30 '18 at 17:11
For one way to "see" what @KM101 said, try writing out all values that $k times 180$ represent in one list, and all values that $k times 360 + 180$ represent in another list, and then make a combined list of everything that shows up in at least one of the first two lists. Make sure you include negative integer values of $k$ when you do this. (Ah ... I see that KM101 was in the middle of doing eactly this when I was writing my comment!)
– Dave L. Renfro
Oct 30 '18 at 17:19
@KM101 how exactly?
– Lyds
Oct 30 '18 at 17:20
Yeah, I’ve added a rather brief explanation with the list. The idea can be applied in both degrees and radians.
– KM101
Oct 30 '18 at 17:20
Check my answer.
– KM101
Oct 30 '18 at 17:20
add a comment |
Those two answers can be “compressed” into one: $x = pi n$.
– KM101
Oct 30 '18 at 17:11
For one way to "see" what @KM101 said, try writing out all values that $k times 180$ represent in one list, and all values that $k times 360 + 180$ represent in another list, and then make a combined list of everything that shows up in at least one of the first two lists. Make sure you include negative integer values of $k$ when you do this. (Ah ... I see that KM101 was in the middle of doing eactly this when I was writing my comment!)
– Dave L. Renfro
Oct 30 '18 at 17:19
@KM101 how exactly?
– Lyds
Oct 30 '18 at 17:20
Yeah, I’ve added a rather brief explanation with the list. The idea can be applied in both degrees and radians.
– KM101
Oct 30 '18 at 17:20
Check my answer.
– KM101
Oct 30 '18 at 17:20
Those two answers can be “compressed” into one: $x = pi n$.
– KM101
Oct 30 '18 at 17:11
Those two answers can be “compressed” into one: $x = pi n$.
– KM101
Oct 30 '18 at 17:11
For one way to "see" what @KM101 said, try writing out all values that $k times 180$ represent in one list, and all values that $k times 360 + 180$ represent in another list, and then make a combined list of everything that shows up in at least one of the first two lists. Make sure you include negative integer values of $k$ when you do this. (Ah ... I see that KM101 was in the middle of doing eactly this when I was writing my comment!)
– Dave L. Renfro
Oct 30 '18 at 17:19
For one way to "see" what @KM101 said, try writing out all values that $k times 180$ represent in one list, and all values that $k times 360 + 180$ represent in another list, and then make a combined list of everything that shows up in at least one of the first two lists. Make sure you include negative integer values of $k$ when you do this. (Ah ... I see that KM101 was in the middle of doing eactly this when I was writing my comment!)
– Dave L. Renfro
Oct 30 '18 at 17:19
@KM101 how exactly?
– Lyds
Oct 30 '18 at 17:20
@KM101 how exactly?
– Lyds
Oct 30 '18 at 17:20
Yeah, I’ve added a rather brief explanation with the list. The idea can be applied in both degrees and radians.
– KM101
Oct 30 '18 at 17:20
Yeah, I’ve added a rather brief explanation with the list. The idea can be applied in both degrees and radians.
– KM101
Oct 30 '18 at 17:20
Check my answer.
– KM101
Oct 30 '18 at 17:20
Check my answer.
– KM101
Oct 30 '18 at 17:20
add a comment |
1 Answer
1
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$$sin x = 0$$
For $n in mathbb{Z}$, $x = pi + 2pi n$ OR $x = 2pi n$.
$$x = pi + 2pi n implies x = …, -5pi, -3pi, -pi,pi, 3pi, 5pi, …$$
$$x = 2pi n implies x = …, -6pi, -4pi, -2pi, 0, 2pi, 4pi, 6pi, …$$
If you noticed, combining them would give all integer multiples of $pi$, so you just combine them.
$$x = pi n$$
You could demonstrate the same idea in degrees: $x = 180+360n$ and $x = 360n$ can be combined to give $x = 180n$.
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$$sin x = 0$$
For $n in mathbb{Z}$, $x = pi + 2pi n$ OR $x = 2pi n$.
$$x = pi + 2pi n implies x = …, -5pi, -3pi, -pi,pi, 3pi, 5pi, …$$
$$x = 2pi n implies x = …, -6pi, -4pi, -2pi, 0, 2pi, 4pi, 6pi, …$$
If you noticed, combining them would give all integer multiples of $pi$, so you just combine them.
$$x = pi n$$
You could demonstrate the same idea in degrees: $x = 180+360n$ and $x = 360n$ can be combined to give $x = 180n$.
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
add a comment |
$$sin x = 0$$
For $n in mathbb{Z}$, $x = pi + 2pi n$ OR $x = 2pi n$.
$$x = pi + 2pi n implies x = …, -5pi, -3pi, -pi,pi, 3pi, 5pi, …$$
$$x = 2pi n implies x = …, -6pi, -4pi, -2pi, 0, 2pi, 4pi, 6pi, …$$
If you noticed, combining them would give all integer multiples of $pi$, so you just combine them.
$$x = pi n$$
You could demonstrate the same idea in degrees: $x = 180+360n$ and $x = 360n$ can be combined to give $x = 180n$.
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
add a comment |
$$sin x = 0$$
For $n in mathbb{Z}$, $x = pi + 2pi n$ OR $x = 2pi n$.
$$x = pi + 2pi n implies x = …, -5pi, -3pi, -pi,pi, 3pi, 5pi, …$$
$$x = 2pi n implies x = …, -6pi, -4pi, -2pi, 0, 2pi, 4pi, 6pi, …$$
If you noticed, combining them would give all integer multiples of $pi$, so you just combine them.
$$x = pi n$$
You could demonstrate the same idea in degrees: $x = 180+360n$ and $x = 360n$ can be combined to give $x = 180n$.
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
$$sin x = 0$$
For $n in mathbb{Z}$, $x = pi + 2pi n$ OR $x = 2pi n$.
$$x = pi + 2pi n implies x = …, -5pi, -3pi, -pi,pi, 3pi, 5pi, …$$
$$x = 2pi n implies x = …, -6pi, -4pi, -2pi, 0, 2pi, 4pi, 6pi, …$$
If you noticed, combining them would give all integer multiples of $pi$, so you just combine them.
$$x = pi n$$
You could demonstrate the same idea in degrees: $x = 180+360n$ and $x = 360n$ can be combined to give $x = 180n$.
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
edited Dec 5 '18 at 4:12
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
answered Oct 30 '18 at 17:19
KM101KM101
5,5911423
5,5911423
add a comment |
add a comment |
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Those two answers can be “compressed” into one: $x = pi n$.
– KM101
Oct 30 '18 at 17:11
For one way to "see" what @KM101 said, try writing out all values that $k times 180$ represent in one list, and all values that $k times 360 + 180$ represent in another list, and then make a combined list of everything that shows up in at least one of the first two lists. Make sure you include negative integer values of $k$ when you do this. (Ah ... I see that KM101 was in the middle of doing eactly this when I was writing my comment!)
– Dave L. Renfro
Oct 30 '18 at 17:19
@KM101 how exactly?
– Lyds
Oct 30 '18 at 17:20
Yeah, I’ve added a rather brief explanation with the list. The idea can be applied in both degrees and radians.
– KM101
Oct 30 '18 at 17:20
Check my answer.
– KM101
Oct 30 '18 at 17:20