Polar equation ordered pairs

[dls1968]

In our textbook, it shows a table of ordered pairs for r=theta when theta is in radians and theta is >= to zero.

The first ordered pair is (0, 0)
The second is (0.8, pi/4)
The third is (1.6, pi/2)

How do they determine these pairs? I believe the x values are different degrees, but how do they get the y values?

All help is appreciated.

 

[soroban]

Hello, dls1968!

You may kick yourself . . .

In our textbook, it shows a table of ordered pairs for $\displaystyle r\,=\,\theta$
when $\displaystyle \theta$ is in radians and $\displaystyle \theta\,\geq\,0$

The first ordered pair is: $\displaystyle (0,\,0)$
The second is: $\displaystyle \left(0.8,\,\frac{\pi}{4}\right)$
The third is: $\displaystyle \left(1.6,\,\frac{\pi}{2}\right)$

How do they determine these pairs?
I believe the x values are different degrees, . No, they're in radians, remember?
but how do they get the y values?

How do we plot points?
We plug in values of $\displaystyle \theta$ and calculate the value of $\displaystyle r$, right?

This function is very simple: $\displaystyle \:r\:=\:\theta$
. . The value of $\displaystyle r$ is $\displaystyle \theta$ itself.

So, when $\displaystyle \theta\,=\,0:\;r\,=\,0$ . . . the first point.

When $\displaystyle \theta\,=\,\frac{\pi}{4}:\;r\,=\,\frac{\pi}{4}\,=\,0.785398163\,\approx\,0.8$ . . . the second point

Got it?