Question

following the instructions for this homework problem given in the image, please help me work on: r=sintheta

Answer 1

To convert the polar equation to a rectangular equation.

Then to graph using rectangualr equation.

Given polar equation is,

`r=\sin \theta`

We know that,

A polar coordinate system, gives the co-ordinates of a point with reference to a

point O and a half line or ray starting at the point O.A point P in the plane, has polar coordinates (r, θ), where r is the distance of the point from the origin and θ is the angle that the ray |OP| makes with the positive x-axis.

To convert from Polar to Cartesian coordinates, we use the identities:

`\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \\ x^2+y^2=r^2 \end{gathered}`

Multiply r to the given polar equation, we get

`r^2=r\sin \theta`

Substitute the values in terms of x and y, we get

`x^2+y^2=y`

we get,

`x^2+y^2-y=0`

On ploting the graph using the above equation we get,