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Select the statements that describe converting the polar coordinates (6, 120°) to rectangular coordinates, (x, y) using technology.

The point is in the second quadrant.

Start by adding 180° to θ.

Substitute 6 for r.

The value of x is 3.

The value of y is approximately 5.196.

(3 right answers)

User Santonu
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2 Answers

3 votes

Answer:

The point is in the second quadrant

Explanation:

User MrAliB
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6 votes

Answer:

The point is in the second quadrant.

Substitute 6 for r.

The value of y is approximately 5.196.

Explanation:

To convert polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

The point is in the second quadrant.

-This statement is true because the polar angle (120°) is in the range of 90° < θ < 180° which correspond to the second quadrant in the cartesian plane.

Start by adding 180° to θ.

This statement is False, because when converting from polar coordinates to rectangular coordinates we don't need to add 180° to the angle, we use the given angle as it is.

Substitute 6 for r.

This statement is true. In this case, the given polar coordinates are (6, 120°), so we substitute 6 for r in the formulas.

The value of x is 3.

This statement is False, to calculate x we use the formula x = r * cos(θ), so in this case x = 6 * cos(120°) = -3, which is not equal to 3.

The value of y is approximately 5.196.

This statement is true, to calculate y we use the formula y = r * sin(θ), so in this case y = 6 * sin(120°) = 6 * 0.866 = 5.196, which is approximately equal to 5.196

User Anthony Mills
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7.3k points