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jimbo said:
what’s a polar function and what’s a complex root marge
Click to expand...
>polar function
instead of getting a y-value for an input x, you get a radius for an input of an angle, usually denoted with theta. it’s based on trigonometric functions, and it uses a circular coordinate plane instead of a rectangular one like the cartesian plane is
>complex root
square root, cube root, etc of complex numbers and finding all solutions
 
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Thrembologist said:
>polar function
instead of getting a y-value for an input x, you get a radius for an input of an angle, usually denoted with theta. it’s based on trigonometric functions, and it uses a circular coordinate plane instead of a rectangular one like the cartesian plane is
>complex root
square root, cube root, etc of complex numbers and finding all solutions
Click to expand...
example of a polar function

IMG_2642.jpeg
 
Niko said:
i dont get it
Click to expand...
it’s based on the equation for a circle x^2 + y^2 = r^2
and also the fact that, if you have a radial line with angle theta, the coordinates of the point on the circle where it falls is given by (r*cos(theta), r*sin(theta).
because of this, you have the relations that x=r*cos(theta)
y=r*sin(theta)
and from the equation of a circle you get that
r=sqrt(x^2 + y^2)

the straight lines on the polar coordinate system represent different angles you can plug into the function
the circles represent different radii that you can get from different angle inputs
 
Thrembologist said:
it’s based on the equation for a circle x^2 + y^2 = r^2
and also the fact that, if you have a radial line with angle theta, the coordinates of the point on the circle where it falls is given by (r*cos(theta), r*sin(theta).
because of this, you have the relations that x=r*cos(theta)
y=r*sin(theta)
and from the equation of a circle you get that
r=sqrt(x^2 + y^2)

the straight lines on the polar coordinate system represent different angles you can plug into the function
the circles represent different radii that you can get from different angle inputs
Click to expand...
also the axial lines represent different angles as well. the line of +x is 0°, the +y is 90°, -x is 180°, -y is 270°
 
Niko said:
what is this
View attachment 4034
Click to expand...
>x^2 +y^2 = r^2
this is the equation of a circle with a radius of r
>radial line
a line going from the center of a circle to a point on its circumference
>angle theta
you know how x is used as a placeholder for any number? theta is like that, but for angles specifically
>(r*cos(theta), r*sin(theta).
this is a point lying on a point on a circle of radius r which, if a radial line was drawn to it, would form the angle theta. cos is the trigonometric function “cosine” and sin is the trigonometric function “sine”
>r=sqrt(x^2 + y^2)
sqrt() is the square root, and this is just the same as an equation of a circle, but solving for r.
>polar coordinate system
look at the graph above, the circular graph thing is the polar coordinate system
 
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