Polar Curves and Trigonometric Functions

The video tutorial explains how to sketch polar curves by plotting points and using the unit circle to calculate cosine values. It demonstrates plotting points directly in polar coordinates and connecting them to form a cardioid shape. The tutorial emphasizes understanding the relationship between R and theta in polar coordinates and provides a step-by-step guide to plotting and connecting points.

What is the brute-force method mentioned for plotting polar curves?

• Using a graphing calculator

• Plotting a series of points by calculating R for various θ values

• Drawing freehand based on intuition

• Using a computer software to simulate the curve

What is the value of R when θ is 0 for the curve R = 1 + cos(θ)?

• 3

• 0

• 1

• 2

How can the unit circle help in computing cosine values for angles?

• By providing a visual representation of angles

• By simplifying the calculation of tangent values

• By allowing direct measurement of angles

• By forming triangles whose sides represent cosine and sine values

What is the cosine of π/4 according to the unit circle method?

• 1

• 1/√2

• 0

• -1/√2

What is the recommended method for plotting points in polar coordinates?

• Using a ruler and compass

• Plotting directly on a Cartesian grid

• Using a connect-the-dots approach in polar coordinates

• Converting polar coordinates to Cartesian coordinates

What happens to the radius as θ increases from 0 to π/2 in the polar curve R = 1 + cos(θ)?

• The radius oscillates

• The radius decreases

• The radius remains constant

• The radius increases

What is the radius when θ is π for the curve R = 1 + cos(θ)?

• 0

• 1

• 2

• 3

What is the shape of the polar curve R = 1 + cos(θ) called?

• Hyperbola

• Parabola

• Cardioid

• Ellipse

How does the radius change as θ goes from π to 3π/2?

• It remains constant

• It decreases from 2 to 1

• It decreases from 1 to 0

• It increases from 0 to 1

What is the final shape of the curve R = 1 + cos(θ) when plotted?

• A cardioid

• A circle

• A straight line

• A spiral