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?