Trigonometric and Polar Functions

Symmetry with respect to the horizontal axis

No symmetry at all

Symmetry with respect to the pole

Symmetry with respect to the line y = x

Undefined coordinates

(1, 0)

(0, $\theta$) for any angle $\theta$

(r, $\pi/2$) where $r > 0$

(0, $\pi/4$)

(2, $\pi/2$)

(1, $\pi$)

(-2, $-\pi/6$)

Cartesian coordinate's points are closer to each other than in polar form.

Polar coordinates use a radius and angle while Cartesian coordinates use x and y values.

Polar coordinates rely on trigonometric functions but Cartesian do not.

Cartesian form doesn't allow for negative values whereas Poler does.

Plot rotates by $\pi$ radians, mirroring over initial petal distribution line through pole.

Each loop size decreases by half keeping total number constant.

Graph compresses radially toward pole while preserving angular symmetry.

The number of loops doubles without affecting their overall size or shape.

A straight line sloped downward.

A horizontal line crossing the y-axis.

A parabola that opens upward.

'b' must be greater than twice the value of 'a'.

'a' must equal zero while 'b' is nonzero.

'a' must be greater than 'b'.

Both 'a' and 'b' must be negative numbers.

A parabola opening towards the right side of the polar grid.

An ellipse aligned along lines $\theta = \frac{\pi}{4}$ and $\theta = -\frac{3\pi}{4}$.

A circle centered at $\left( \frac{\pi}{4}, \frac{\pi}{4} \right)$.

A straight line through the pole making a 45-degree angle with the positive x-axis.

Plotting the graph and looking for the point where $r = 0$.

Performing polar-to-cartesian conversion to find coordinates at the origin.

Utilizing conic section techniques to determine the point of intersection.

Plotting the graph and locating the peak value of the r function.

Continuous

Discrete

Discontinuous

Intermittent