AP PRECALCULUS; RATES OF CHANGE IN POLAR GRAPHS. UNIT 3.15

The graph of the polar function 𝑟 = 𝑓(𝜃), is given the polar coordinate system. Which of the following defines 𝑓(𝜃) for 0 ≤ 𝜃 ≤ 2𝜋 ?

• 𝑓(𝜃) = 3 − 5 sin(𝜃)

• 𝑓(𝜃) = 4 − 4 sin(𝜃)

• �(𝜃) = 2 − 2 sin(𝜃)

• �(𝜃) = 2 − 6 sin(𝜃)

• The graph of 𝑟 = 𝑓(𝜃) is a spiral with increasing radius

• The graph of 𝑟 = 𝑓(𝜃) is a spiral with decreasing radius

What is the primary focus of this video lesson regarding polar functions?

• Calculating the area enclosed by polar curves

• Determining the rate of change of the radius (r)

• Converting polar coordinates to Cartesian coordinates

• Finding the arc length of polar curves

When observing the animated polar graph of r = 6sin(3θ), what does the red line segment represent?

• The tangent line to the curve

• The angle θ from the positive x-axis

• The radius r, or distance from the pole

• The instantaneous velocity of the point

For the function r = 6sin(3θ), what is the behavior of 'r' in the interval (0, π/6)?

• r is negative and increasing

• r is positive and decreasing

• r is positive and increasing

• r is negative and decreasing

In the interval (π/6, π/3) for r = 6sin(3θ), how does 'r' behave?

• r is positive and decreasing

• r is negative and increasing

• r is positive and increasing

• r is negative and decreasing

What is the behavior of 'r' in the interval (π/3, π/2) for r = 6sin(3θ)?

• r is positive and increasing

• r is negative and decreasing

• r is positive and decreasing

• r is negative and increasing

For r = 6sin(3θ), what is the behavior of 'r' in the interval (π/2, 2π/3)?

• r is negative and increasing

• r is positive and decreasing

• r is negative and decreasing

• r is positive and increasing

If 'r' is positive and the function f(θ) is increasing, what is happening to the distance from the pole?

• The distance is decreasing (getting closer)

• The distance is increasing (getting farther away)

• The distance remains constant

• The distance becomes negative

Which of the following is the graph of the polar function 𝑟 = 𝑓(𝜃), where 𝑓(𝜃) = 4 − 4 cos 𝜃, in the polar coordinate system for 0 ≤ 𝜃 ≤ 2𝜋 ?

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