Video Transcript

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

Weโ€™re interested in the point
๐ถ. And we want to know its polar
coordinates. Remember, these are of the form ๐‘Ÿ,
๐œƒ. 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‘Ÿ, thatโ€™s the length of our half line, and ๐œƒ, the angle that this
half line makes with the positive ๐‘ฅ-axis. And since weโ€™re told that ๐œƒ must
be greater than negative ๐œ‹ and less than or equal to ๐œ‹, weโ€™re going to travel in a
clockwise direction.

Now, ๐‘Ÿ 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‘Ÿ must be equal to one. But what about the angle ๐œƒ? We know that a full turn is two ๐œ‹
radians. And half a turn is ๐œ‹ radians. This half a turn is split into 12
subintervals. So each subinterval must represent
๐œ‹ by 12 radians. Our half line travels three of
these subintervals. Thatโ€™s three lots of ๐œ‹ by 12,
which is ๐œ‹ by four. But weโ€™re travelling in a clockwise
direction. So our value of ๐œƒ for the polar
coordinates of ๐ถ is negative ๐œ‹ by four. And the polar coordinates of ๐ถ are
therefore one, negative ๐œ‹ by four. Notice that had we travelled in a
counterclockwise direction, weโ€™d have, of course, an angle of seven, ๐œ‹ by four. But thatโ€™s outside of the range of
๐œƒ given.

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