@@dalalaljazzaf8139 I know I'm (just a bit) late, but you know that (x^2)+(y^2)=1, so we can plug in 1 for that part of the equation, leaving us with 1-2ycos(theta)=0. Then, turn the "y" into rsin(theta), to get 1-2rsin(theta)cos(theta)=0. To get "r" on it's own, you must divide both sides by 1-sin(2theta)[as 2sin(theta)cos(theta) is our double- angle sin identity], but diving zero by any number yields 0, so you would get r=0, final answer. Again, sorry that this is late, but here ya go.
In all reality, it doesn't matter. You can even shift the origin around if you wanted to and rotate the plane counter-clockwise 117 degrees. It's all just a matter of convenience :) Out of convention, we just relate the cosine function to the x-axis and the sine function to the y-axis. Again, out of convenience.
i can't understand this because for example i want to convert cartesian equation of hyperbola " x²/a² - y²/b² = 1 " into its parametric equation x= aSecθ , y = bTanθ please someone help me about this
Sin is your X axis, Cos is your y axis. you want them to be controlled by t, so sin(t) and Cos(t). x and y are being squared, so therefore their resultant quantity needs to be squared.
You sir deserve a nobel prize
Thank you so much! This helped me a ton and now I can finish my math homework :)
i was really starving for this sum , thank you bro
THANK YOU SOO MUCH
only found single video for this
had to look for this topic because my calculator doesn't graph relations, only functions, Thank you
I too think it would be better to make x=4cost.
Lol nice input
This is great, but what is the domain for parameter t?
For x²+y²=16, does it matter if the parametric equation of x is, x=4cost instead of x=4sint?
If you want to trace it clockwise then sin otherwise cos
@@ayushbisht6756 please explain what you mean by this
what about (x−x(za))2+(y−y(za))2=r2 ??? it has a z as well xd
nice video- quick and easy to understand
is there more than one solution to each one of these questions ???
see señor
Extremely helpful, thanks.
Parametric form for points in 2d space???
is there a way to convert
x^2 + y^2 - 2y cosx = 0
into parametric ?
did you find a way?
@@dalalaljazzaf8139 I know I'm (just a bit) late, but you know that (x^2)+(y^2)=1, so we can plug in 1 for that part of the equation, leaving us with 1-2ycos(theta)=0. Then, turn the "y" into rsin(theta), to get 1-2rsin(theta)cos(theta)=0. To get "r" on it's own, you must divide both sides by 1-sin(2theta)[as 2sin(theta)cos(theta) is our double- angle sin identity], but diving zero by any number yields 0, so you would get r=0, final answer. Again, sorry that this is late, but here ya go.
Why is x equal to 4 sin t? Shouldn't b equal to 4 cos t?
Doesn't matter...as long as one is sin and the other is cos.
In all reality, it doesn't matter. You can even shift the origin around if you wanted to and rotate the plane counter-clockwise 117 degrees. It's all just a matter of convenience :)
Out of convention, we just relate the cosine function to the x-axis and the sine function to the y-axis. Again, out of convenience.
Thank you very much.
Thanks 👍
i can't understand this because for example i want to convert cartesian equation of hyperbola " x²/a² - y²/b² = 1 " into its parametric equation x= aSecθ , y = bTanθ
please someone help me about this
do you know how now? because i want to know
@@dalalaljazzaf8139 for a parabola you use sinh(x) and cosh(x) instead of sin and cos. Also why would you want to use sec and tan? Makes no sense.
Tysm
how to solve : x^4 - y^4 -z^4 = 1
There is actually a rational parametrization for the equation x^2+y^2= 16 it is [4(1-t^2)/(1+t^2), 8t/(1+t^2)]
Can someone tell me the answer
What is the parametric eq. Of this cartesian one?
X=3
x=t
y=0t
x=rcos y=rsin
1:15 what
Sin is your X axis, Cos is your y axis. you want them to be controlled by t, so sin(t) and Cos(t). x and y are being squared, so therefore their resultant quantity needs to be squared.
@@Kitsyfluff oh ok thank you
crap -