Converting Cartesian Coordinates to Polar Coordinates

The video tutorial explains how to convert Cartesian coordinates (-4, 2) to polar coordinates (r, theta). It begins by plotting the point on the Cartesian plane and sketching a reference triangle. The distance r is calculated using the Pythagorean theorem, resulting in r = 2√5. The angle theta is determined using the arctangent function, with adjustments for the correct quadrant, resulting in theta ≈ 2.6779 radians. The final polar coordinates are (2√5, 2.6779 radians).

What is the range of theta in polar coordinates?

• 0 to 2π radians, including both

• 0 to 2π radians, excluding both

• 0 to 2π radians, including 0 but excluding 2π

• 0 to 2π radians, excluding 0 but including 2π

In which direction do we rotate to find the angle theta in polar coordinates?

• Clockwise from the positive y-axis

• Counterclockwise from the negative y-axis

• Counterclockwise from the positive x-axis

• Clockwise from the negative x-axis

What is the formula for calculating the distance r in polar coordinates?

• r = √(x^2 + y^2)

• r = x^2 + y^2

• r = √(x + y)

• r = x + y

How do you simplify the square root of 20?

• 5√2

• 2√5

• √20

• 4√5

What is the initial output range of the arctangent function?

• 0 to π

• −π/2 to π/2

• 0 to 2π

• −π to π

Which quadrant is the angle theta located in for the given Cartesian coordinates?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the reference angle for theta if the arctangent gives −0.4636 radians?

• π − 0.4636 radians

• 0.4636 radians

• −0.4636 radians

• π + 0.4636 radians

How do you adjust the angle found by arctangent to find theta in the second quadrant?

• Subtract π from the negative angle

• Add 2π to the negative angle

• Subtract 2π from the negative angle

• Add π to the negative angle

What is the final value of theta in radians for the polar coordinates?

• 3.1416 radians

• 0.4636 radians

• 2.6779 radians

• 1.6779 radians

What are the polar coordinates for the Cartesian point (-4, 2)?

• (2√5, 2.6779 radians)

• (2√5, 1.6779 radians)

• (√20, 2.6779 radians)

• (√20, 1.6779 radians)