VIDEO NOTES: Polar Coordinates: Example 5: Straight Lines

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In this video I go over another example on polar coordinates and this time look at how to make straight line segments that pass through the origin. The example I look at is graphing the straight line segment formed by the polar equation θ = 1 radian. This means that for every distance from the origin r, the angle remains the same which is θ = 1 radian. Thus we get a straight line with a consistent angle. The polar coordinate system shows how it is very easy to formulate straight line segments that pass through the origin, again because of the circular nature of its definition. This is a quick video to illustrate the polar coordinate system in graphing straight lines, so make sure to watch it!

Polar Coordinates Playlist

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Example: Sketch the polar curve θ = 1

This curve consists of all points (r , θ) such that the polar angle θ is 1 radian.

It is thus a straight line that passes through the origin O and makes an angle of 1 radian with the polar axis, as shown below:

Notice that the points (r , 1) on the line with r > 0 are in the first quadrant, whereas those with r < 0 are in the third quadrant (i.e. the opposite quadrant).