6 precal questions pls help

1.

Find the rectangular coordinates of the point with the polar coordinates (3, 3 divided by 2 pi ). (1 point)

2.

Find the rectangular coordinates of the point with the polar coordinates ordered pair 3 comma 5 pi divided by 3 . (1 point)

ordered pair negative 3 divided by 2 comma 3 divided by 2

ordered pair 3 divided by 2 comma negative 3 square root 3 divided by 2

ordered pair negative 3 square root 3 divided by 2 comma 3 divided by 2

ordered pair 3 divided by 2 comma negative 3 divided by 2

3.

Find all polar coordinates of point P where P = ordered pair 5 comma pi divided by 3 . (2 points)

(5, pi divided by 3 + nπ) or (-5, pi divided by 3 + nπ)

(5, pi divided by 3 + (2n + 1)π) or (-5, pi divided by 3 + 2nπ)

(5, pi divided by 3 + 2nπ) or (-5, pi divided by 3 + (2n + 1)π)

(5, pi divided by 3 + 2nπ) or (-5, pi divided by 3 + 2nπ)

4.

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°. (2 points)

(4 square root of 2 , 45°), (-4 square root of 2 , 225°)

(4 square root of 2 , 135°), (-4 square root of 2 , 315°)

(4 square root of 2 , 225°), (-4 square root of 2 , 45°)

(4 square root of 2 , 315°), (-4 square root of 2 , 135°)

5.

Use your grapher to determine which of the graphs matches the polar equation r = 1 + 2 cos θ. (2 points)

a circular graph with an inner loop on the left

a circle tangent to the y-axis, symmetric about the axis, and lying in quadrants one and four

a circular graph with an indentation on the left to the origin

a graph of four loops originating at the origin lying on and symmetric about the and y-axes

6.

Find all polar coordinates of point P = (6, 31°). (2 points)

 
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