### Video Transcript

Consider the points plotted on the

graph. Write down the polar coordinates of

๐ถ, giving the angle ๐ in the range ๐ is greater than negative ๐ and less than or

equal to ๐.

Weโre interested in the point

๐ถ. And we want to know its polar

coordinates. Remember, these are of the form ๐,

๐. Letโs add a half line or a ray from

the pole to point ๐ถ. Our job is going to be to work out

the value of ๐, thatโs the length of our half line, and ๐, the angle that this

half line makes with the positive ๐ฅ-axis. And since weโre told that ๐ must

be greater than negative ๐ and less than or equal to ๐, weโre 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. Thatโs three lots of ๐ by 12,

which is ๐ by four. But weโre travelling in a clockwise

direction. So our value of ๐ for the polar

coordinates of ๐ถ is negative ๐ by four. And the polar coordinates of ๐ถ are

therefore one, negative ๐ by four. Notice that had we travelled in a

counterclockwise direction, weโd have, of course, an angle of seven, ๐ by four. But thatโs outside of the range of

๐ given.