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Example Questions
Example Question #71 : Polar Coordinates
Which polar-coordinate point is not the same as the rectangular point ?
Plotting this point creates a triangle in quadrant I:
Using our knowledge of Special Right Triangles, we can conclude that the angle is and the radius/hypotenuse of this triangle is . Our polar coordinates are therefore , so we can eliminate that as a choice since we know it works.
Looking at the unit circle [or just the relevant parts] can give us a sense of what happens when the angles and/or the radii are negative:
Now we can easily see that the angle would correspond with our angle of , so works.
We can see that if our radius is negative we'd want to start off at the angle , so the point works.
As we can see from looking at this excerpt from the unit circle, another way of writing the angle would be to write , so the point works.
The only one that does not work would be because that would place us in quadrant II rather than I like we want.
Example Question #72 : Polar Coordinates
Which of the following is a set of polar coordinates for the point with the rectangular coordinates .
The relation between polar coordinates and rectangular coordinates is given by and .
You can plug in each of the choices for and and see which pair gives the rectangular coordinate .
The answer turns out to be .
Alternatively, you can find by the equation
, thus
.
As for finding , you can use the equation
, and since
.
Thus, the polar coordinate is .
Example Question #21 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the point to polar form
First, find r using pythagorean theorem,
Then we can find theta by doing the inverse tangent of y over x:
Since this point is in quadrant II, add 180 degrees to get
Example Question #22 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the following rectangular coordinates to polar coordinates:
To convert from rectangular coordinates to polar coordinates :
Using the rectangular coordinates given by the question,
The polar coordinates are
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