Precalculus : Convert Polar Coordinates To Rectangular Coordinates

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Example Question #655 : Pre Calculus

Convert the polar coordinates  to rectangular form.

Possible Answers:

 

Correct answer:

 

Explanation:

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 #1 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #2 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #3 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #4 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #5 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #6 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular form:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #7 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #8 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #9 : Convert Polar Coordinates To Rectangular Coordinates

How could you express  in rectangular coordinates?

Possible Answers:

Correct answer:

Explanation:

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

.

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