This triangle is important for solving many problems related to polar coordinates.

From it we get the following important relationships:

`x=r*cos(theta)`

`y=r*sin(theta)`

`r^2=x^2+y^2`

`tan(theta)=y/x`

In polar coordinates we write `r` as a function of `theta`, `r=f(theta)`.

Now consider the equation `x=r*cos(theta)`. If we differentiate with respect to `theta`, the we get `(dx)/(d theta)=(dr)/(d theta)*cos(theta)-r*sin(theta)`.

Similarly, `(dy)/(d theta)=(dr)/(d theta)*sin(theta)+r*cos(theta)`.

These relationships will be useful when looking at slope and arc length, which are concepts from rectangular coordinates.

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