Converting Rectangular Coordinates to Polar Form

The video tutorial explains the differences between polar and rectangular coordinates, focusing on how to convert from rectangular to polar coordinates using specific formulas. It provides two examples to illustrate the conversion process, including calculations for radius and angle, and discusses the importance of understanding the quadrant for accurate results.

What coordinate system uses circles and angles to locate points?

• Rectangular coordinates

• Hexagonal coordinates

• Polar coordinates

• Cartesian coordinates

Which theorem is used to derive the formula for the radius in polar coordinates?

• Fundamental theorem of algebra

• Binomial theorem

• Theorem of calculus

• Pythagorean theorem

What is the formula for the radius R in polar coordinates?

• R = √(x² + y²)

• R = x/y

• R = x + y

• R = x² + y²

How do you calculate the angle θ in polar coordinates?

• θ = y/x

• θ = sin⁻¹(y/x)

• θ = cos⁻¹(y/x)

• θ = tan⁻¹(y/x)

For the point (-3, 4), what is the calculated radius in polar coordinates?

• 3

• 4

• 7

• 5

What adjustment is made to the angle when converting a point in the second quadrant?

• Add 90 degrees

• Subtract 90 degrees

• Subtract 180 degrees

• Add 180 degrees

What is the polar coordinate angle for the point (-3, 4) after adjustment?

• 127 degrees

• 53.1 degrees

• 233 degrees

• 310 degrees

In the second example, what is the radius for the point (2, 2√3)?

• 4

• 6

• 2

• 8

What trigonometric function is used to find the angle in polar coordinates?

• Sine

• Cosine

• Tangent

• Cotangent

What is the angle in radians for the point (2, 2√3) in polar coordinates?

• π/2

• π/4

• π/6

• π/3