Angle between vector and x-axis in specific intervals
$begingroup$
Given a vector going from a point $(x_0,y_0)$ to $(x_1,y_1)$ in a regular 2D-plane (i.e. an $hat{x}$-axis pointing right and a $hat{y}$-axis pointing up), I want to determine the angle between the vector and the $hat{x}$-axis.
When the vector is in the first and second quadrant, the angle should be between $[0,-pi]$, and between $[0,pi]$ when it is in the third and forth quadrant. To clarify, a vector pointing in positive and negative $hat{y}$-direction should have angle $-frac{pi}{2}$ and $frac{pi}{2}$, respectively.
What is the expression for the angle?
angle
asked Jan 9 at 14:35
ryekosryekos
204
$endgroup$
add a comment |
$begingroup$
Given a vector going from a point $(x_0,y_0)$ to $(x_1,y_1)$ in a regular 2D-plane (i.e. an $hat{x}$-axis pointing right and a $hat{y}$-axis pointing up), I want to determine the angle between the vector and the $hat{x}$-axis.
When the vector is in the first and second quadrant, the angle should be between $[0,-pi]$, and between $[0,pi]$ when it is in the third and forth quadrant. To clarify, a vector pointing in positive and negative $hat{y}$-direction should have angle $-frac{pi}{2}$ and $frac{pi}{2}$, respectively.
What is the expression for the angle?
angle
asked Jan 9 at 14:35
ryekosryekos
204
$endgroup$
add a comment |
$begingroup$
Given a vector going from a point $(x_0,y_0)$ to $(x_1,y_1)$ in a regular 2D-plane (i.e. an $hat{x}$-axis pointing right and a $hat{y}$-axis pointing up), I want to determine the angle between the vector and the $hat{x}$-axis.
When the vector is in the first and second quadrant, the angle should be between $[0,-pi]$, and between $[0,pi]$ when it is in the third and forth quadrant. To clarify, a vector pointing in positive and negative $hat{y}$-direction should have angle $-frac{pi}{2}$ and $frac{pi}{2}$, respectively.
What is the expression for the angle?
angle
asked Jan 9 at 14:35
ryekosryekos
204
$endgroup$
Given a vector going from a point $(x_0,y_0)$ to $(x_1,y_1)$ in a regular 2D-plane (i.e. an $hat{x}$-axis pointing right and a $hat{y}$-axis pointing up), I want to determine the angle between the vector and the $hat{x}$-axis.
When the vector is in the first and second quadrant, the angle should be between $[0,-pi]$, and between $[0,pi]$ when it is in the third and forth quadrant. To clarify, a vector pointing in positive and negative $hat{y}$-direction should have angle $-frac{pi}{2}$ and $frac{pi}{2}$, respectively.
What is the expression for the angle?
angle
angle
asked Jan 9 at 14:35
ryekosryekos
204
asked Jan 9 at 14:35
ryekosryekos
204
asked Jan 9 at 14:35
ryekosryekos
204
asked Jan 9 at 14:35
ryekosryekos
204
asked Jan 9 at 14:35
ryekosryekos
204
204
add a comment |
add a comment |
1 Answer
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$begingroup$
The angle from the vector to the $x$ axis is equal to minus of the angle between the $x$ axis and the vector. You have for this second angle $$tantheta=frac{y_1-y_0}{x_1-x_0}$$
The first guess would be to use the arctangent. Notice that if you take the ratio, you cannot distinguish between angles in quadrants $2$ and $4$, or between angles in quadrants $1$ and $3$. For many computer programming languages, there is a function called $rm{atan2}$ or $rm{arctan2}$. The arguments are $y_1-y_0$ and $x_1-x_0$. You can find a formal description on wikipedia.
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
The angle from the vector to the $x$ axis is equal to minus of the angle between the $x$ axis and the vector. You have for this second angle $$tantheta=frac{y_1-y_0}{x_1-x_0}$$
The first guess would be to use the arctangent. Notice that if you take the ratio, you cannot distinguish between angles in quadrants $2$ and $4$, or between angles in quadrants $1$ and $3$. For many computer programming languages, there is a function called $rm{atan2}$ or $rm{arctan2}$. The arguments are $y_1-y_0$ and $x_1-x_0$. You can find a formal description on wikipedia.
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
$endgroup$
add a comment |
$begingroup$
The angle from the vector to the $x$ axis is equal to minus of the angle between the $x$ axis and the vector. You have for this second angle $$tantheta=frac{y_1-y_0}{x_1-x_0}$$
The first guess would be to use the arctangent. Notice that if you take the ratio, you cannot distinguish between angles in quadrants $2$ and $4$, or between angles in quadrants $1$ and $3$. For many computer programming languages, there is a function called $rm{atan2}$ or $rm{arctan2}$. The arguments are $y_1-y_0$ and $x_1-x_0$. You can find a formal description on wikipedia.
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
$endgroup$
add a comment |
$begingroup$
The angle from the vector to the $x$ axis is equal to minus of the angle between the $x$ axis and the vector. You have for this second angle $$tantheta=frac{y_1-y_0}{x_1-x_0}$$
The first guess would be to use the arctangent. Notice that if you take the ratio, you cannot distinguish between angles in quadrants $2$ and $4$, or between angles in quadrants $1$ and $3$. For many computer programming languages, there is a function called $rm{atan2}$ or $rm{arctan2}$. The arguments are $y_1-y_0$ and $x_1-x_0$. You can find a formal description on wikipedia.
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
$endgroup$
The angle from the vector to the $x$ axis is equal to minus of the angle between the $x$ axis and the vector. You have for this second angle $$tantheta=frac{y_1-y_0}{x_1-x_0}$$
The first guess would be to use the arctangent. Notice that if you take the ratio, you cannot distinguish between angles in quadrants $2$ and $4$, or between angles in quadrants $1$ and $3$. For many computer programming languages, there is a function called $rm{atan2}$ or $rm{arctan2}$. The arguments are $y_1-y_0$ and $x_1-x_0$. You can find a formal description on wikipedia.
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
answered Jan 9 at 15:31
AndreiAndrei
13.4k21230
13.4k21230
add a comment |
add a comment |
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