Converting Cartesian to Polar Coordinates

The video tutorial explains how to convert Cartesian coordinates (6, -2) to polar coordinates. It begins by plotting the point on a coordinate plane and then uses a reference triangle and the Pythagorean theorem to calculate the distance r. The angle theta is determined using the arctangent function, with adjustments made to ensure it falls within the specified interval. The final polar coordinates are calculated as 2√10 and approximately 5.9614 radians.

What is the interval for theta in polar coordinates?

• -2π to 2π

• 0 to 2π

• 0 to π

• -π to π

In which quadrant is the reference triangle located for the point (6, -2)?

• Second quadrant

• Fourth quadrant

• First quadrant

• Third quadrant

What is the formula used to calculate the distance r in polar coordinates?

• r = x + y

• r = √(x^2 + y^2)

• r = √(x + y)

• r = x^2 + y^2

How is the tangent of theta calculated in the reference triangle?

• Tangent theta = x^2/y^2

• Tangent theta = y/x

• Tangent theta = y^2/x^2

• Tangent theta = x/y

What is the range of the arctangent function?

• -π to π

• 0 to 2π

• -π/2 to π/2

• 0 to π

What is the simplified form of the distance r for the point (6, -2)?

• √40

• 2√5

• 4√10

• 2√10

Which function is used to find the reference angle for theta?

• Arcsine

• Arctangent

• Cosine

• Sine

What adjustment is made to the reference angle to fit it into the interval from 0 to 2π?

• Subtract π

• Add π

• Subtract 2π

• Add 2π

What is the approximate value of theta in radians after adjustment?

• 6.2832

• 0.3218

• 3.1416

• 5.9614

What are the final polar coordinates for the Cartesian point (6, -2)?

• (2√10, 0.3218)

• (√40, 5.9614)

• (2√10, 5.9614)

• (2√5, 0.3218)