mariechap89 said:Express the following in cartesian curves in polar form
i) 4x-5y=2
Not sure how to do this
ii) (x-3)^2+(y-4)^2=25
r=9cos16(theta)
Is this correct ?
Any help would be great
Cartesian coordinates are a rectangular coordinate system where a point is located based on its distance from the x-axis and y-axis. Polar coordinates are a circular coordinate system where a point is located based on its distance from the origin and its angle relative to a reference axis.
To convert a cartesian equation to polar form, you can use the following equations:
x = r cos(theta)
y = r sin(theta)
r = √(x^2 + y^2)
theta = arctan(y/x)
where r is the distance from the origin, and theta is the angle relative to the x-axis.
The equation for a circle in polar form is r = a, where a is the radius of the circle.
To plot a polar curve, you can plot points using the polar coordinates (r, theta) and then connect them to create a curve. You can also use a polar graphing calculator or software to plot the curve.
Some common polar curves include circles, cardioids, limaçons, and lemniscates. Other more complex polar curves include roses, spirals, and hypocycloids.