Polar Coordinates and Derivatives

Mr. Bean introduces polar graphs and their derivatives, explaining the conversion between polar and rectangular coordinates. He demonstrates graphing polar equations using a calculator and discusses calculating slopes of tangents to polar curves. The lesson concludes with finding horizontal and vertical tangents in polar graphs.

What is the directed distance from the origin to a point in the polar coordinate system called?

• Hypotenuse

• Angle

• Theta

• Radius

In the polar coordinate system, what does a negative radius indicate?

• The point is closer to the origin

• The point is in the opposite direction

• The angle is negative

• The radius is zero

Which trigonometric function relates the y-coordinate to the radius and angle in polar coordinates?

• Sine

• Tangent

• Secant

• Cosine

How do you convert a point from polar form to rectangular form?

• Add the radius and angle

• Divide the radius by the angle

• Multiply the radius by cosine and sine of the angle

• Use the Pythagorean theorem

What is the equation of a vertical line in rectangular coordinates?

• y = c

• r = θ

• x = a

• y = mx + b

When graphing polar equations on a calculator, what must the equation be in terms of?

• x

• y

• r

• θ

What is the first step in finding the slope of a curve in polar form?

• Use the Pythagorean theorem

• Find the radius

• Convert to rectangular coordinates

• Calculate the angle

In the context of polar derivatives, what does the product rule apply to?

• Neither

• Only the denominator

• Only the numerator

• Both numerator and denominator

What must be true for a horizontal tangent line in polar coordinates?

• The radius is zero

• The angle is zero

• The numerator of the derivative is zero

• The denominator of the derivative is zero

What indicates a vertical tangent line in polar coordinates?

• The angle is zero

• The radius is zero

• The denominator of the derivative is zero

• The numerator of the derivative is zero