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