This is really helpful video for me to understand this conversation in my ongoing college study because I face it but unable to understand properly, so now this video will help me a lot
The functions cos(theta) = x/r and sin(theta) = y/r are definitions of the trig functions in a circle (assume r ≠ 0) and thus work in every quadrant. It is a result of the definitions that the absolute value of cos(theta) in this definition is the same as cos(alpha), using the normal right-triangle trig definitions with alpha being the reference angle for theta (smallest positive angle with either side of the x-axis).
yes, it works. The only trick is to check the polar angle first to see which quadrant the point is in, and adjust signs as necessary when using the trig functions. Essentially, sin and cos give you a magnitude and sign, but you must verify the direction (sign) based on the quadrant, which is based on the given angle.
If the angle is 30 how is it that the radius is -4 which is r and which is also the hypotenuse of the right triangle? Am a bit confused. I thought that r represented the distance of the hypotenuse which is the radius.....I was also taught that the radius is always positive. So what exactly does -4 represent?
Which coordinate system do I like better, between(circular) polar and rectangular? Honestly, depends on the situation. E.g.: I can think of lots of situations in classical (Newtonian) mechanics where rectangular coordinates are more convenient. Same goes for Special Relativity. On the other hand, I can think of situations in Quantum Mechanics where (circular) polar is wayyy more convenient.
+blackpenredpen how do you determine the polar domain of theta for functions like y=x^2-1? It seems like there is an undefined range +/- pi/2 ...at least in the real numbers. Thanks
Obviously each system has its advantages according to the problème you want to solve, but generally I tend to prefer rectangular coordinates because each point in space can be identified uniquely.
Since you asked us which system we prefer: I prefer the rectangular coördinates, though for some problems the polar coördinates can be preferable. But I wonder do you, bprp, ever educate _quaternions_ ?
Hey blackpen redpen, can you do a video on what would be the formula to solve delta d with regards to time velocity acceleration and a constant jerk (m/s^3)?
Hey. I have two whishes: 1. Find the positive minimum of pi-function, the lowest positive factorial - it's round about 0.462 (I hope for an exciting result) 2. Can you tell us something about the number 0.1234567891011121314.... (All the positive integers in a line) Is there some interesting result, for which these number converge? Thank you very much Mr Mathematik
Hi ! Firstly thank you so much for this super video and this goood explication I have a problem with an integral which is : (i)^2x *(cos(arctg√x+ln2x))
Hi, good day! Can you help me to solve this: Draw a 2 unit ray from the origin at an angle of 60 degree. Converting from polar to rectangular coordinates. What is the point (2, 60 degree) in rectangular coordinates? I want to know the solution. Many thanks! I subscribed to ur TH-cam channel coz I like the way how u explained it. More power and Godbless 😇
If you are thinking about r as the length, then it is a positive number and the minus sign is the direction. Putting these two together you have the r coordinate.
Sure, you can change the angle. If all you need is a point, it doesn't matter. But now you know how you move on a line when the angle is fixed. Put the angle as zero and you are moving along the x axis, like you are used to. Try to find what the angle should be to move along the y axis. (Ever wondered why you are not asking how x can be negative?)
If x is real there are no solutions, if x is complex (a+bi) I found this system but I can't solve it on the fly {a=cos(a)/e^b ; b = sin(a)/e^b } . Wolfram Alpha gives approx a=0.58 and b=0.37 .
This is really helpful video for me to understand this conversation in my ongoing college study because I face it but unable to understand properly, so now this video will help me a lot
I have started saying "isn't it" and I blame this channel
: )
Objection, leading. Strike.the question and restate.
omg ive been waiting for this for so long!
Excellent video. Love the supreme jacket🔥
Amir Zidan thanks!!!
The formula for conversion was demonstrated to work in the first quadrant, but why should it work in the other three?
The functions cos(theta) = x/r and sin(theta) = y/r are definitions of the trig functions in a circle (assume r ≠ 0) and thus work in every quadrant. It is a result of the definitions that the absolute value of cos(theta) in this definition is the same as cos(alpha), using the normal right-triangle trig definitions with alpha being the reference angle for theta (smallest positive angle with either side of the x-axis).
yes, it works. The only trick is to check the polar angle first to see which quadrant the point is in, and adjust signs as necessary when using the trig functions. Essentially, sin and cos give you a magnitude and sign, but you must verify the direction (sign) based on the quadrant, which is based on the given angle.
If the angle is 30 how is it that the radius is -4 which is r and which is also the hypotenuse of the right triangle?
Am a bit confused. I thought that r represented the distance of the hypotenuse which is the radius.....I was also taught that the radius is always positive. So what exactly does -4 represent?
Which coordinate system do I like better, between(circular) polar and rectangular? Honestly, depends on the situation. E.g.: I can think of lots of situations in classical (Newtonian) mechanics where rectangular coordinates are more convenient. Same goes for Special Relativity. On the other hand, I can think of situations in Quantum Mechanics where (circular) polar is wayyy more convenient.
+blackpenredpen how do you determine the polar domain of theta for functions like y=x^2-1? It seems like there is an undefined range +/- pi/2 ...at least in the real numbers. Thanks
Obviously each system has its advantages according to the problème you want to solve, but generally I tend to prefer rectangular coordinates because each point in space can be identified uniquely.
Much better explanation than most.
I'm disappointed there was no Chen Lu. I imagine it's something between DBZ and focusing ones chi or ki.
Since you asked us which system we prefer: I prefer the rectangular coördinates, though for some problems the polar coördinates can be preferable.
But I wonder do you, bprp, ever educate _quaternions_ ?
Hey blackpen redpen, can you do a video on what would be the formula to solve delta d with regards to time velocity acceleration and a constant jerk (m/s^3)?
Ty you for the explanation! Lovin that supreme jacket as well!
Was in my exam :)
pro tip : watch series on flixzone. Me and my gf have been using it for watching loads of movies recently.
Thank you so much, and I prefer the rectangular over the polar coordinates.
So helpful!! Thank you
Excellent 👌🏽
You teach so well! :D
thank you!
What mic are you using?
Hey. I have two whishes: 1. Find the positive minimum of pi-function, the lowest positive factorial - it's round about 0.462 (I hope for an exciting result)
2. Can you tell us something about the number
0.1234567891011121314....
(All the positive integers in a line)
Is there some interesting result, for which these number converge?
Thank you very much Mr Mathematik
Sandmann great idea
Sandmann I
Is r negative or positive if x is negative and y is positive? Also, is r negative or positive if x is positive and y is negative?
Wait, nevermind. It depends on the angle theta obviously. 😅
Hi ! Firstly thank you so much for this super video and this goood explication
I have a problem with an integral which is :
(i)^2x *(cos(arctg√x+ln2x))
I like the way you speak.
"Use the Chen Lu! "
WOW! thank you very much
Solve pls √(x+y)-√x-√y+2=0 for natural x,y
Hi, good day! Can you help me to solve this: Draw a 2 unit ray from the origin at an angle of 60 degree. Converting from polar to rectangular coordinates. What is the point (2, 60 degree) in rectangular coordinates? I want to know the solution. Many thanks! I subscribed to ur TH-cam channel coz I like the way how u explained it. More power and Godbless 😇
Rectangular co-ordinate system
Hey Black pen Red Pen
Please integrate 1/(×+e^×)
And (cos(x^2)/(×^2))
Thanks
how could r be negative?
I agree this is weird, but it's just a matter of convention
If you are thinking about r as the length, then it is a positive number and the minus sign is the direction. Putting these two together you have the r coordinate.
Simos why don't you just change the angle?
Sure, you can change the angle. If all you need is a point, it doesn't matter. But now you know how you move on a line when the angle is fixed. Put the angle as zero and you are moving along the x axis, like you are used to. Try to find what the angle should be to move along the y axis. (Ever wondered why you are not asking how x can be negative?)
you forgot the second solution for the negative square root of 3, which would give the first cuadrant solution.
He's not taking a square root. Cosine is a function i.e. gives only one value.
supreme gang
Woohoo!
I think he put wrong measurements while looking for the cosine of 30
If e^(xi)=x find x
If x is real there are no solutions, if x is complex (a+bi) I found this system but I can't solve it on the fly {a=cos(a)/e^b ; b = sin(a)/e^b } . Wolfram Alpha gives approx a=0.58 and b=0.37 .
There are no solutions in real world, aren't there?
The answer is may be in imaginary world
I have started talking super fast, now even i.can't understand what i am saying😅😅😜....
E' la prima volta che vedo un'interpretazione negativa di un raggio!