Exploring the Archimedean Spiral with Desmos

This video tutorial explores the Archimedean spiral using Desmos. It begins with setting up Desmos to graph the polar equation r = nθ, including changing the grid to polar and adding sliders for variables. The tutorial demonstrates how to trace the spiral from 0 to 4π and then to 12π, showing the effect of changing the variable n on the spiral's direction and size. The video concludes with a summary of how the values of n and θ affect the spiral's properties.

What is the primary tool used in this lesson to explore the Archimedean spiral?

• Microsoft Excel

• GeoGebra

• Desmos

• Wolfram Alpha

Which equation represents the Archimedean spiral in this lesson?

• r = θ/n

• r = nθ

• r = n + θ

• r = n/θ

What is the initial interval for θ in the exploration of the spiral?

• 0 to 12π

• 0 to 6π

• 0 to 4π

• 0 to 2π

How can you change the graph style to dashed in Desmos?

• By using the wrench icon

• By changing the color to orange

• By clicking and holding the circle next to the equation

• By clicking the gear icon

What happens to the spiral when the value of 'n' is set to zero?

• The spiral becomes a straight line

• The spiral rotates clockwise

• The spiral disappears

• The spiral becomes a circle

In which direction does the spiral trace when both θ and n are positive?

• Clockwise

• Outward

• Counterclockwise

• Inward

What effect does a negative 'n' have on the spiral's direction?

• It makes the spiral disappear

• It does not affect the direction

• It becomes clockwise

• It remains counterclockwise

What determines the direction of the spiral?

• The size of the graph

• The color of the graph

• The absolute value of θ

• The sign of n and θ

What happens to the spiral as the absolute value of n increases?

• The spiral shrinks

• The spiral enlarges

• The spiral rotates faster

• The spiral changes color

What is the relationship between nθ and the spiral's direction?

• If nθ is negative, the spiral is counterclockwise

• If nθ is positive, the spiral is clockwise

• If nθ is positive, the spiral is counterclockwise

• If nθ is zero, the spiral is counterclockwise