Convert the polar equation to rectangular form. (Use x for x and y for y as necessary.) Sketch the graph of this equation. (Do this on paper. Your instructor may ask you to turn in this graph.)r = -7

The polar equation given is r = -7.

To convert this to rectangular form, we use the relationship between polar and rectangular coordinates. The polar coordinates (r, θ) and rectangular coordinates (x, y) are related as follows:

x = r cos θ y = r sin θ

However, in this case, the polar equation is simply r = -7, which means the radius is -7. This is a circle with a radius of 7 units but in the opposite direction.

In rectangular coordinates, a circle with radius 7 is represented as:

x² + y² = r²

Substituting r = -7, we get:

x² + y² = (-7)² x² + y² = 49

This is the rectangular form of the given polar equation.

As for sketching the graph, it will be a circle centered at the origin (0,0) with a radius of 7 units. However, because r = -7, the direction is reversed, meaning that points are plotted in the opposite direction of the standard polar direction. This doesn't change the appearance of the circle in the rectangular coordinate system, but it does change the direction in which you'd move around the circle in the polar coordinate system.