### Video Transcript

Consider the points plotted on the
graph. Write down the polar coordinates of
πΆ, giving the angle π in the range π is greater than negative π and less than or
equal to π.

Weβre interested in the point
πΆ. And we want to know its polar
coordinates. Remember, these are of the form π,
π. Letβs add a half line or a ray from
the pole to point πΆ. Our job is going to be to work out
the value of π, thatβs the length of our half line, and π, the angle that this
half line makes with the positive π₯-axis. And since weβre told that π must
be greater than negative π and less than or equal to π, weβre going to travel in a
clockwise direction.

Now, π 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 π must be equal to one. But what about the angle π? We know that a full turn is two π
radians. And half a turn is π radians. This half a turn is split into 12
subintervals. So each subinterval must represent
π by 12 radians. Our half line travels three of
these subintervals. Thatβs three lots of π by 12,
which is π by four. But weβre travelling in a clockwise
direction. So our value of π for the polar
coordinates of πΆ is negative π by four. And the polar coordinates of πΆ are
therefore one, negative π by four. Notice that had we travelled in a
counterclockwise direction, weβd have, of course, an angle of seven, π by four. But thatβs outside of the range of
π given.