Finding x and y coordinates from the angle
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I have a robot that I am trying to program. I came up with a way to find by how many degrees my arm moved but I want to find a relative $(x , y)$ coordinates. I think that I found the formula:
$x = D_1 * cos(D_1theta)$
and $y = D_1 * sin(D_1theta)$.
$D_1$ is the length of my robot arm. $D_1theta$ is the degree that it moved in radians.
Why is it $cos$ and $sin$, I don’t get it.
trigonometry python
edited Nov 23 '18 at 19:48
Timothy Cho
789519
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
$endgroup$
add a comment |
$begingroup$
I have a robot that I am trying to program. I came up with a way to find by how many degrees my arm moved but I want to find a relative $(x , y)$ coordinates. I think that I found the formula:
$x = D_1 * cos(D_1theta)$
and $y = D_1 * sin(D_1theta)$.
$D_1$ is the length of my robot arm. $D_1theta$ is the degree that it moved in radians.
Why is it $cos$ and $sin$, I don’t get it.
trigonometry python
edited Nov 23 '18 at 19:48
Timothy Cho
789519
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
$endgroup$
$begingroup$
Do you know what $sin$ and $cos$ is? That is fairly standard results.
$endgroup$
– Henrik
Nov 23 '18 at 18:26
add a comment |
$begingroup$
I have a robot that I am trying to program. I came up with a way to find by how many degrees my arm moved but I want to find a relative $(x , y)$ coordinates. I think that I found the formula:
$x = D_1 * cos(D_1theta)$
and $y = D_1 * sin(D_1theta)$.
$D_1$ is the length of my robot arm. $D_1theta$ is the degree that it moved in radians.
Why is it $cos$ and $sin$, I don’t get it.
trigonometry python
edited Nov 23 '18 at 19:48
Timothy Cho
789519
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
$endgroup$
I have a robot that I am trying to program. I came up with a way to find by how many degrees my arm moved but I want to find a relative $(x , y)$ coordinates. I think that I found the formula:
$x = D_1 * cos(D_1theta)$
and $y = D_1 * sin(D_1theta)$.
$D_1$ is the length of my robot arm. $D_1theta$ is the degree that it moved in radians.
Why is it $cos$ and $sin$, I don’t get it.
trigonometry python
trigonometry python
edited Nov 23 '18 at 19:48
Timothy Cho
789519
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
edited Nov 23 '18 at 19:48
Timothy Cho
789519
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
edited Nov 23 '18 at 19:48
Timothy Cho
789519
edited Nov 23 '18 at 19:48
Timothy Cho
789519
edited Nov 23 '18 at 19:48
Timothy Cho
789519
789519
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
asked Nov 23 '18 at 18:17
Kyrylo KalashnikovKyrylo Kalashnikov
32
32
$begingroup$
Do you know what $sin$ and $cos$ is? That is fairly standard results.
$endgroup$
– Henrik
Nov 23 '18 at 18:26
add a comment |
$begingroup$
Do you know what $sin$ and $cos$ is? That is fairly standard results.
$endgroup$
– Henrik
Nov 23 '18 at 18:26
$begingroup$
Do you know what $sin$ and $cos$ is? That is fairly standard results.
$endgroup$
– Henrik
Nov 23 '18 at 18:26
$begingroup$
Do you know what $sin$ and $cos$ is? That is fairly standard results.
$endgroup$
– Henrik
Nov 23 '18 at 18:26
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Just try to visualize it on a circle with radius $r$. (Like a unit circle except the radius can be anything.)
For an angle $theta$ drawn from the origin, you form a right-triangle with hypotenuse $r$. The horizontal leg (call it $x$) is adjacent to angle $theta$ while the vertical leg (call it $y$) is opposite to angle $theta$. Thus, you can conlude
$$cos theta = frac{x}{r} implies x = rcos theta$$
$$sin theta = frac{y}{r} implies y = rsin theta$$
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
$endgroup$
$begingroup$
I dont understand how can you relate angle of rotation to x , y coordinates
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:47
$begingroup$
Is it like a Cartesian plane with x and y?
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:53
$begingroup$
Yes. All you’re doing is resolving $r$ into an $x$-component and a $y$-component, followed by using the definition of sine and cosine to find the values of $x$ and $y$.
$endgroup$
– KM101
Nov 23 '18 at 19:56
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Just try to visualize it on a circle with radius $r$. (Like a unit circle except the radius can be anything.)
For an angle $theta$ drawn from the origin, you form a right-triangle with hypotenuse $r$. The horizontal leg (call it $x$) is adjacent to angle $theta$ while the vertical leg (call it $y$) is opposite to angle $theta$. Thus, you can conlude
$$cos theta = frac{x}{r} implies x = rcos theta$$
$$sin theta = frac{y}{r} implies y = rsin theta$$
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
$endgroup$
$begingroup$
I dont understand how can you relate angle of rotation to x , y coordinates
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:47
$begingroup$
Is it like a Cartesian plane with x and y?
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:53
$begingroup$
Yes. All you’re doing is resolving $r$ into an $x$-component and a $y$-component, followed by using the definition of sine and cosine to find the values of $x$ and $y$.
$endgroup$
– KM101
Nov 23 '18 at 19:56
add a comment |
$begingroup$
Just try to visualize it on a circle with radius $r$. (Like a unit circle except the radius can be anything.)
For an angle $theta$ drawn from the origin, you form a right-triangle with hypotenuse $r$. The horizontal leg (call it $x$) is adjacent to angle $theta$ while the vertical leg (call it $y$) is opposite to angle $theta$. Thus, you can conlude
$$cos theta = frac{x}{r} implies x = rcos theta$$
$$sin theta = frac{y}{r} implies y = rsin theta$$
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
$endgroup$
$begingroup$
I dont understand how can you relate angle of rotation to x , y coordinates
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:47
$begingroup$
Is it like a Cartesian plane with x and y?
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:53
$begingroup$
Yes. All you’re doing is resolving $r$ into an $x$-component and a $y$-component, followed by using the definition of sine and cosine to find the values of $x$ and $y$.
$endgroup$
– KM101
Nov 23 '18 at 19:56
add a comment |
$begingroup$
Just try to visualize it on a circle with radius $r$. (Like a unit circle except the radius can be anything.)
For an angle $theta$ drawn from the origin, you form a right-triangle with hypotenuse $r$. The horizontal leg (call it $x$) is adjacent to angle $theta$ while the vertical leg (call it $y$) is opposite to angle $theta$. Thus, you can conlude
$$cos theta = frac{x}{r} implies x = rcos theta$$
$$sin theta = frac{y}{r} implies y = rsin theta$$
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
$endgroup$
Just try to visualize it on a circle with radius $r$. (Like a unit circle except the radius can be anything.)
For an angle $theta$ drawn from the origin, you form a right-triangle with hypotenuse $r$. The horizontal leg (call it $x$) is adjacent to angle $theta$ while the vertical leg (call it $y$) is opposite to angle $theta$. Thus, you can conlude
$$cos theta = frac{x}{r} implies x = rcos theta$$
$$sin theta = frac{y}{r} implies y = rsin theta$$
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
answered Nov 23 '18 at 18:26
KM101KM101
5,8711423
5,8711423
$begingroup$
I dont understand how can you relate angle of rotation to x , y coordinates
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:47
$begingroup$
Is it like a Cartesian plane with x and y?
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:53
$begingroup$
Yes. All you’re doing is resolving $r$ into an $x$-component and a $y$-component, followed by using the definition of sine and cosine to find the values of $x$ and $y$.
$endgroup$
– KM101
Nov 23 '18 at 19:56
add a comment |
$begingroup$
I dont understand how can you relate angle of rotation to x , y coordinates
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:47
$begingroup$
Is it like a Cartesian plane with x and y?
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:53
$begingroup$
Yes. All you’re doing is resolving $r$ into an $x$-component and a $y$-component, followed by using the definition of sine and cosine to find the values of $x$ and $y$.
$endgroup$
– KM101
Nov 23 '18 at 19:56
$begingroup$
I dont understand how can you relate angle of rotation to x , y coordinates
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:47
$begingroup$
I dont understand how can you relate angle of rotation to x , y coordinates
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:47
$begingroup$
Is it like a Cartesian plane with x and y?
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:53
$begingroup$
Is it like a Cartesian plane with x and y?
$endgroup$
– Kyrylo Kalashnikov
Nov 23 '18 at 19:53
$begingroup$
Yes. All you’re doing is resolving $r$ into an $x$-component and a $y$-component, followed by using the definition of sine and cosine to find the values of $x$ and $y$.
$endgroup$
– KM101
Nov 23 '18 at 19:56
$begingroup$
Yes. All you’re doing is resolving $r$ into an $x$-component and a $y$-component, followed by using the definition of sine and cosine to find the values of $x$ and $y$.
$endgroup$
– KM101
Nov 23 '18 at 19:56
add a comment |
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$begingroup$
Do you know what $sin$ and $cos$ is? That is fairly standard results.
$endgroup$
– Henrik
Nov 23 '18 at 18:26