formula for getting the normlized X and Y values of a given degrees from a linear function
I have a number which we'll call α in degrees that represent the angle of a linear function with the X axis. for example when α is 0 the linear function is on the X axis , when α is 360 the linear function is on the X axis.
when α is 90 the linear function is on the Y axis. and so on.
I want to get from the linear function
y = αx
the X of y = 1, and the Y of x = 1.
and I am not sure how can I do that.
can anyone post a quick forumla for calc such a thing? does it have a name ?
I know trigo may be needed to transfer degrees for a slope that represent the value of y for X = 1.
linear-algebra functions trigonometry
asked Dec 9 '18 at 20:27
tomer zeitune
31
|
show 8 more comments
I have a number which we'll call α in degrees that represent the angle of a linear function with the X axis. for example when α is 0 the linear function is on the X axis , when α is 360 the linear function is on the X axis.
when α is 90 the linear function is on the Y axis. and so on.
I want to get from the linear function
y = αx
the X of y = 1, and the Y of x = 1.
and I am not sure how can I do that.
can anyone post a quick forumla for calc such a thing? does it have a name ?
I know trigo may be needed to transfer degrees for a slope that represent the value of y for X = 1.
linear-algebra functions trigonometry
asked Dec 9 '18 at 20:27
tomer zeitune
31
When $alpha =90°$, it doesn't necessarily mean that the linear function is on the y-Axis. It rather shows that it is parallel to the y-axis
– Dr. Mathva
Dec 9 '18 at 20:41
Is $alpha$ given, or do you get the function and have to calculate it?
– Dr. Mathva
Dec 9 '18 at 20:42
alpha is given.
– tomer zeitune
Dec 9 '18 at 20:55
What's the problem then? You would have: $$text{X of y=1}=frac{1}{alpha}$$ and $$text{Y of x=1}=alpha$$ Or am I missing something?
– Dr. Mathva
Dec 9 '18 at 20:57
Alpha is in degrees how do I transfer that to a slope (Y value for X = 1) ?
– tomer zeitune
Dec 9 '18 at 21:49
|
show 8 more comments
I have a number which we'll call α in degrees that represent the angle of a linear function with the X axis. for example when α is 0 the linear function is on the X axis , when α is 360 the linear function is on the X axis.
when α is 90 the linear function is on the Y axis. and so on.
I want to get from the linear function
y = αx
the X of y = 1, and the Y of x = 1.
and I am not sure how can I do that.
can anyone post a quick forumla for calc such a thing? does it have a name ?
I know trigo may be needed to transfer degrees for a slope that represent the value of y for X = 1.
linear-algebra functions trigonometry
asked Dec 9 '18 at 20:27
tomer zeitune
31
I have a number which we'll call α in degrees that represent the angle of a linear function with the X axis. for example when α is 0 the linear function is on the X axis , when α is 360 the linear function is on the X axis.
when α is 90 the linear function is on the Y axis. and so on.
I want to get from the linear function
y = αx
the X of y = 1, and the Y of x = 1.
and I am not sure how can I do that.
can anyone post a quick forumla for calc such a thing? does it have a name ?
I know trigo may be needed to transfer degrees for a slope that represent the value of y for X = 1.
linear-algebra functions trigonometry
linear-algebra functions trigonometry
asked Dec 9 '18 at 20:27
tomer zeitune
31
asked Dec 9 '18 at 20:27
tomer zeitune
31
asked Dec 9 '18 at 20:27
tomer zeitune
31
asked Dec 9 '18 at 20:27
tomer zeitune
31
asked Dec 9 '18 at 20:27
tomer zeitune
31
31
When $alpha =90°$, it doesn't necessarily mean that the linear function is on the y-Axis. It rather shows that it is parallel to the y-axis
– Dr. Mathva
Dec 9 '18 at 20:41
Is $alpha$ given, or do you get the function and have to calculate it?
– Dr. Mathva
Dec 9 '18 at 20:42
alpha is given.
– tomer zeitune
Dec 9 '18 at 20:55
What's the problem then? You would have: $$text{X of y=1}=frac{1}{alpha}$$ and $$text{Y of x=1}=alpha$$ Or am I missing something?
– Dr. Mathva
Dec 9 '18 at 20:57
Alpha is in degrees how do I transfer that to a slope (Y value for X = 1) ?
– tomer zeitune
Dec 9 '18 at 21:49
|
show 8 more comments
When $alpha =90°$, it doesn't necessarily mean that the linear function is on the y-Axis. It rather shows that it is parallel to the y-axis
– Dr. Mathva
Dec 9 '18 at 20:41
Is $alpha$ given, or do you get the function and have to calculate it?
– Dr. Mathva
Dec 9 '18 at 20:42
alpha is given.
– tomer zeitune
Dec 9 '18 at 20:55
What's the problem then? You would have: $$text{X of y=1}=frac{1}{alpha}$$ and $$text{Y of x=1}=alpha$$ Or am I missing something?
– Dr. Mathva
Dec 9 '18 at 20:57
Alpha is in degrees how do I transfer that to a slope (Y value for X = 1) ?
– tomer zeitune
Dec 9 '18 at 21:49
When $alpha =90°$, it doesn't necessarily mean that the linear function is on the y-Axis. It rather shows that it is parallel to the y-axis
– Dr. Mathva
Dec 9 '18 at 20:41
When $alpha =90°$, it doesn't necessarily mean that the linear function is on the y-Axis. It rather shows that it is parallel to the y-axis
– Dr. Mathva
Dec 9 '18 at 20:41
Is $alpha$ given, or do you get the function and have to calculate it?
– Dr. Mathva
Dec 9 '18 at 20:42
Is $alpha$ given, or do you get the function and have to calculate it?
– Dr. Mathva
Dec 9 '18 at 20:42
alpha is given.
– tomer zeitune
Dec 9 '18 at 20:55
alpha is given.
– tomer zeitune
Dec 9 '18 at 20:55
What's the problem then? You would have: $$text{X of y=1}=frac{1}{alpha}$$ and $$text{Y of x=1}=alpha$$ Or am I missing something?
– Dr. Mathva
Dec 9 '18 at 20:57
What's the problem then? You would have: $$text{X of y=1}=frac{1}{alpha}$$ and $$text{Y of x=1}=alpha$$ Or am I missing something?
– Dr. Mathva
Dec 9 '18 at 20:57
Alpha is in degrees how do I transfer that to a slope (Y value for X = 1) ?
– tomer zeitune
Dec 9 '18 at 21:49
Alpha is in degrees how do I transfer that to a slope (Y value for X = 1) ?
– tomer zeitune
Dec 9 '18 at 21:49
|
show 8 more comments
1 Answer
1
active
oldest
votes
Claim:
If $alpha$ is the inclination angle of a linear function, then the slope of the function is $arctan alpha$
Proof
Let $Delta ABC$ be the slope triangle of the function, with $[AB]$ lying on the x-axis. Denote by $m$ the slope of the function and by $alpha$ the angle of the linear function with the x-axis. Since $angle CBA=90°$, we can tell $$tan(angle BAC)=tan(alpha)=frac{BC}{AB}=m$$
Let then simply $$X=frac{1}{tan(alpha)}$$ and $$Y=tan(alpha)$$
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
add a comment |
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1 Answer
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1 Answer
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oldest
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oldest
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active
oldest
votes
Claim:
If $alpha$ is the inclination angle of a linear function, then the slope of the function is $arctan alpha$
Proof
Let $Delta ABC$ be the slope triangle of the function, with $[AB]$ lying on the x-axis. Denote by $m$ the slope of the function and by $alpha$ the angle of the linear function with the x-axis. Since $angle CBA=90°$, we can tell $$tan(angle BAC)=tan(alpha)=frac{BC}{AB}=m$$
Let then simply $$X=frac{1}{tan(alpha)}$$ and $$Y=tan(alpha)$$
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
add a comment |
Claim:
If $alpha$ is the inclination angle of a linear function, then the slope of the function is $arctan alpha$
Proof
Let $Delta ABC$ be the slope triangle of the function, with $[AB]$ lying on the x-axis. Denote by $m$ the slope of the function and by $alpha$ the angle of the linear function with the x-axis. Since $angle CBA=90°$, we can tell $$tan(angle BAC)=tan(alpha)=frac{BC}{AB}=m$$
Let then simply $$X=frac{1}{tan(alpha)}$$ and $$Y=tan(alpha)$$
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
add a comment |
Claim:
If $alpha$ is the inclination angle of a linear function, then the slope of the function is $arctan alpha$
Proof
Let $Delta ABC$ be the slope triangle of the function, with $[AB]$ lying on the x-axis. Denote by $m$ the slope of the function and by $alpha$ the angle of the linear function with the x-axis. Since $angle CBA=90°$, we can tell $$tan(angle BAC)=tan(alpha)=frac{BC}{AB}=m$$
Let then simply $$X=frac{1}{tan(alpha)}$$ and $$Y=tan(alpha)$$
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
Claim:
If $alpha$ is the inclination angle of a linear function, then the slope of the function is $arctan alpha$
Proof
Let $Delta ABC$ be the slope triangle of the function, with $[AB]$ lying on the x-axis. Denote by $m$ the slope of the function and by $alpha$ the angle of the linear function with the x-axis. Since $angle CBA=90°$, we can tell $$tan(angle BAC)=tan(alpha)=frac{BC}{AB}=m$$
Let then simply $$X=frac{1}{tan(alpha)}$$ and $$Y=tan(alpha)$$
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
answered Dec 9 '18 at 22:51
Dr. Mathva
919316
919316
add a comment |
add a comment |
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When $alpha =90°$, it doesn't necessarily mean that the linear function is on the y-Axis. It rather shows that it is parallel to the y-axis
– Dr. Mathva
Dec 9 '18 at 20:41
Is $alpha$ given, or do you get the function and have to calculate it?
– Dr. Mathva
Dec 9 '18 at 20:42
alpha is given.
– tomer zeitune
Dec 9 '18 at 20:55
What's the problem then? You would have: $$text{X of y=1}=frac{1}{alpha}$$ and $$text{Y of x=1}=alpha$$ Or am I missing something?
– Dr. Mathva
Dec 9 '18 at 20:57
Alpha is in degrees how do I transfer that to a slope (Y value for X = 1) ?
– tomer zeitune
Dec 9 '18 at 21:49