Polar Coordinates and Curves Online Quiz Questions

A point has rectangular coordinates (3, 4). What is its nonnegative polar radius r?

Which polar coordinate represents the same point as (−2, π/3)?

The curve r = 4 cos θ is unchanged when θ is replaced by −θ. About which line does this establish symmetry?

Which two conditions generally identify a horizontal tangent of a polar curve at a parameter value? Select all correct choices.

For finding the area of one petal of r = 3 sin(2θ), which statements are correct? Select all correct choices.

True or false: For r = f(θ), the polar arc-length integrand is sqrt(r² + (dr/dθ)²).

True or false: For any rectangular point (x, y), calculating arctan(y/x) alone always gives the correct polar angle.

For the polar curve r = 1 + sin θ, what is the exact value of r at θ = π/2?

What is the exact arc length of the cardioid r = 2 + 2 cos θ traced once for 0 ≤ θ ≤ 2π?

For the curve r = 1 + sin θ at θ = π/2, derive the slope dy/dx and determine the tangent line. Explain why the derivative formula is valid at this parameter value.

What geometric curve is represented by the polar equation r = 4 cos θ?

True or false: For a polar curve, if $dx/d\theta=0$ and $dy/d\theta\ne0$ at a point, then the curve generally has a vertical tangent there.

The polar equation $r=4\cos\theta$ represents a circle. What is the $x$-coordinate of its center?

What curve family is represented by an equation of the form $r=a\theta$?

What is the area of one petal of the rose curve $r=3\sin(2\theta)$?

A region lies inside $r=3$ and outside $r=1$ for $0\le\theta\le\pi/2$. What is its area?

Which rectangular equation is equivalent to the polar equation r=4 sin θ?

For the polar curve r=θ, what is dy/dx at θ=π/2?