Question Video: Graphing Polar Coordinates | Nagwa Question Video: Graphing Polar Coordinates | Nagwa

# Question Video: Graphing Polar Coordinates Mathematics • Third Year of Secondary School

## Join Nagwa Classes

Consider the points plotted on the graph. Write down the polar coordinates of πΆ, giving the angle π in the range βπ < π β€ π.

01:31

### Video Transcript

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

Weβre interested in the point πΆ. And we want to know its polar coordinates. Remember, these are of the form π, π. Letβs add a half line or a ray from the pole to point πΆ. Our job is going to be to work out the value of π, thatβs the length of our half line, and π, the angle that this half line makes with the positive π₯-axis. And since weβre told that π must be greater than negative π and less than or equal to π, weβre 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. Thatβs three lots of π by 12, which is π by four. But weβre travelling in a clockwise direction. So our value of π for the polar coordinates of πΆ is negative π by four. And the polar coordinates of πΆ are therefore one, negative π by four. Notice that had we travelled in a counterclockwise direction, weβd have, of course, an angle of seven, π by four. But thatβs outside of the range of π given.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions