Polar Equations and Derivatives

The video tutorial explains how to find the slope and equation of a tangent line for a given polar equation. It begins with calculating the x and y coordinates when theta equals pi/2, followed by deriving the slope using derivatives. The tutorial then formulates the equation of the tangent line and demonstrates graphing the polar equation. An additional example problem is solved to reinforce the concepts.

What is the polar equation given in the problem?

• r = 2 + 3 sin(theta)

• r = 2 + 3 cos(theta)

• r = 3 + 2 cos(theta)

• r = 3 - 2 sin(theta)

What is the value of r when theta is pi/2?

• 0

• 1

• 3

• 2

How do you calculate x in polar coordinates?

• x = r sin(theta)

• x = r

• x = r cos(theta)

• x = r tan(theta)

Which rule is used to find the derivative of x with respect to theta?

• Quotient Rule

• Chain Rule

• Product Rule

• Power Rule

What is the derivative of cosine with respect to theta?

• sin(theta)

• -sin(theta)

• cos(theta)

• -cos(theta)

What is the slope of the tangent line when evaluated?

• 2/3

• 1/2

• 2

• 3/2

What is the equation of the tangent line in slope-intercept form?

• y = 2/3x + 3

• y = 3x + 2/3

• y = 2x + 3/2

• y = 3/2x + 2

Where does the polar equation touch the x-axis?

• At 0 and 2

• At 3 and 6

• At 2 and 4

• At 1 and 5

What is the new polar equation in the second example?

• r = 3 - 2 sin(theta)

• r = 2 - 3 cos(theta)

• r = 3 + 2 sin(theta)

• r = 2 + 3 cos(theta)

What is the value of r when theta is pi in the second example?

• 3

• 2

• 1

• 4