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Example Question #1 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular form.
We begin by recalling that polar coordinates are expressed in the form , where
is the radius (the distance from the origin to the point) and
is the angle formed between the postive x-axis and the radius.
We can find our x-coordinate and y-coordinate in rectangular form quite easily by keeping in mind two equations.
or
or
Substituting in both of these gives respectively
Therefore, the rectangular coordinates of our point are
Example Question #2 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular coordinates:
To convert polar coordinates to rectangular coordinates
,
Using the information given in the question,
The rectangular coordinates are
Example Question #3 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular coordinates:
To convert polar coordinates to rectangular coordinates
,
Using the information given in the question,
The rectangular coordinates are
Example Question #4 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular coordinates:
To convert polar coordinates to rectangular coordinates
,
Using the information given in the question,
The rectangular coordinates are
Example Question #5 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular coordinates:
To convert polar coordinates to rectangular coordinates
,
Using the information given in the question,
The rectangular coordinates are
Example Question #6 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular coordinates:
To convert polar coordinates to rectangular coordinates
,
Using the information given in the question,
The rectangular coordinates are
Example Question #7 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular form:
To convert polar coordinates to rectangular coordinates
,
Using the information given in the question,
The rectangular coordinates are
Example Question #8 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Convert the polar coordinates to rectangular coordinates:
To convert polar coordinates to rectangular coordinates
,
Using the information given in the question,
The rectangular coordinates are
Example Question #9 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
How could you express in rectangular coordinates?
The polar coordinates given have an angle of but a negative radius, so our coordinates are located in quadrant III.
This means x and y are both negative. You can figure out these x and y coordinates using trigonometric ratios, or since the angle is , special right triangles.
The hypotenuse of this triangle is 5, but in the special right triangle it's 2, so we know we're multiplying each side by .
That makes the x-coordinate or adjacent side be
and the y-coordinate or opposite side be
.
In this case, once again, both are negative, so our answer is
.
Example Question #1 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
How could you express in rectangular coordinates?
Round to the nearest hundredth.
In order to determine the rectangular coordinates, look at the triangle representing the polar coordinates:
We can see that both x and y are positive. We can figure out the x-coordinate by using the cosine:
multiply both sides by 10.
We can figure out the y-coordinate by using the sine:
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