### Video Transcript

Consider the points plotted on the
graph. Write down the polar coordinates of
๐ถ, giving the angle ๐ in the range ๐ is greater than negative ๐ and less than or
equal to ๐.

Weโre interested in the point
๐ถ. And we want to know its polar
coordinates. Remember, these are of the form ๐,
๐. Letโs add a half line or a ray from
the pole to point ๐ถ. Our job is going to be to work out
the value of ๐, thatโs the length of our half line, and ๐, the angle that this
half line makes with the positive ๐ฅ-axis. And since weโre told that ๐ must
be greater than negative ๐ and less than or equal to ๐, weโre going to travel in a
clockwise direction.

Now, ๐ is quite easy to
calculate. We follow the grid around. And we see that the point is
located exactly one unit from the pole. So ๐ must be equal to one. But what about the angle ๐? We know that a full turn is two ๐
radians. And half a turn is ๐ radians. This half a turn is split into 12
subintervals. So each subinterval must represent
๐ by 12 radians. Our half line travels three of
these subintervals. Thatโs three lots of ๐ by 12,
which is ๐ by four. But weโre travelling in a clockwise
direction. So our value of ๐ for the polar
coordinates of ๐ถ is negative ๐ by four. And the polar coordinates of ๐ถ are
therefore one, negative ๐ by four. Notice that had we travelled in a
counterclockwise direction, weโd have, of course, an angle of seven, ๐ by four. But thatโs outside of the range of
๐ given.

You are watching: Question Video: Graphing Polar Coordinates. Info created by GBee English Center selection and synthesis along with other related topics.